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%I #103 Feb 06 2021 22:05:42
%S 929,1615,1958,3330,4016,4359,5731,6417,6760,8132,8818,9161,10533,
%T 11219,11562,12934,13620,13963,15335,16021,16364,17736,18422,18765,
%U 20137,20823,21166,22538,23224,23567,24939,25282,25625,25968,27340,28026,28369,29741,30427
%N 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.
%C Note that [ 24*k-1 == 0 (mod 7^3) ] iff [ k == 243 (mod 7^3) ].
%C Related to a general congruence of Ramanujan about the partition function. See A340757.
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F { k : A214411(A000041(k)) >= A214411(24*k-1) >= 3 }. - _Alois P. Heinz_, Feb 01 2021
%e 929 is a term because A000041(929) = 1378663636778122744608506419570 = 2 * 5 * 7^3 * 17 * 19 * 139 * 8952552536856941584067 and 24 * 929 - 1 = 5 * 7^3 * 13.
%t Select[243 + 343*Range[100], IntegerExponent[PartitionsP[#], 7] >= IntegerExponent[24*# - 1, 7] &] (* _Amiram Eldar_, Feb 05 2021 *)
%o (PARI) seq(x) = {my( k = -100, N=0); while(N < x, k += 343;
%o if(valuation(numbpart(k), 7) >= valuation(24*k-1, 7), print1(k", "); N++)) };
%o seq(100); \\ Gives the first 100 terms of the sequence.
%Y Cf. A000041, A214411, A340757.
%K nonn
%O 1,1
%A _Washington Bomfim_, Feb 01 2021
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