{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:22:30Z","timestamp":1760059350086,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,7]],"date-time":"2025-06-07T00:00:00Z","timestamp":1749254400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the authors derive some believed-to-be new recursion and explicit formulas for the generalized Ramanujan numbers \u03c4s(n)(s\u2208N\u222a{\u22121}), where, as usual, N is the set of positive integers. The authors consider the associated partition functions and derive connections of the Eisenstein series with the numbers \u03c4s(n). Several related corollaries and consequences of each of the presented results are also given. The paper concludes by presenting an open problem that is related to one of these results.<\/jats:p>","DOI":"10.3390\/axioms14060451","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T06:46:01Z","timestamp":1749451561000},"page":"451","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Class of the Generalized Ramanujan Tau Numbers and Their Associated Partition Functions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1491-165X","authenticated-orcid":false,"given":"Aleksandar","family":"Petojevi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Education, University of Novi Sad, Podgori\u010dka 4, 25000 Sombor, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari M.","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"},{"name":"Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ 1007 Baku, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-6885-4394","authenticated-orcid":false,"given":"Sonja","family":"Orli\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Education, University of Novi Sad, Podgori\u010dka 4, 25000 Sombor, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1215\/S0012-7094-47-01436-1","article-title":"The vanishing of Ramanujan\u2019s function \u03c4(n)","volume":"14","author":"Lehmer","year":"1947","journal-title":"Duke Math. 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