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 A340957 Numbers k such that 24*k-1 has at least three factors 7 and the partition function evaluated at k has at least the same number of factors 7 as 24*k-1. 3
 929, 1615, 1958, 3330, 4016, 4359, 5731, 6417, 6760, 8132, 8818, 9161, 10533, 11219, 11562, 12934, 13620, 13963, 15335, 16021, 16364, 17736, 18422, 18765, 20137, 20823, 21166, 22538, 23224, 23567, 24939, 25282, 25625, 25968, 27340, 28026, 28369, 29741, 30427 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Note that [ 24*k-1 == 0 (mod 7^3) ] iff [ k == 243 (mod 7^3) ]. Related to a general congruence of Ramanujan about the partition function. See A340757. LINKS FORMULA { k : A214411(A000041(k)) >= A214411(24*k-1) >= 3 }. - Alois P. Heinz, Feb 01 2021 EXAMPLE 929 is a term because A000041(929) = 1378663636778122744608506419570 = 2 * 5 * 7^3 * 17 * 19 * 139 * 8952552536856941584067 and 24 * 929 - 1 = 5 * 7^3 * 13. MATHEMATICA Select[243 + 343*Range, IntegerExponent[PartitionsP[#], 7] >= IntegerExponent[24*# - 1, 7] &] (* Amiram Eldar, Feb 05 2021 *) PROG (PARI) seq(x) = {my( k = -100, N=0); while(N < x, k += 343; if(valuation(numbpart(k), 7) >= valuation(24*k-1, 7), print1(k", "); N++)) }; seq(100); \\ Gives the first 100 terms of the sequence. CROSSREFS Cf. A000041, A214411, A340757. Sequence in context: A237229 A219526 A249535 * A289727 A290967 A109184 Adjacent sequences:  A340954 A340955 A340956 * A340958 A340959 A340960 KEYWORD nonn AUTHOR Washington Bomfim, Feb 01 2021 STATUS approved

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Last modified January 20 09:55 EST 2022. Contains 350471 sequences. (Running on oeis4.)