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A262542 List of numbers arising in Theorem 5 of Morris Newman's "Further identities and congruences for the coefficients of modular forms".

%I A262542 #15 Jul 24 2023 13:00:20
%S A262542 6,10,17,18,24,27,57,68,69,74,90,95,98,103,123,127,131,163,179,197,
%T A262542 204,210,238,239,249,250,253,256,258,259,270,274,278,282,292,326,349,
%U A262542 359,360,364,373,374,376,378,400,407,424,425,447,448,451,454,474,480,492,493,507,558,563,569
%N A262542 List of numbers arising in Theorem 5 of Morris Newman's "Further identities and congruences for the coefficients of modular forms".
%C A262542 These are exactly the numbers n such that A010819(n) = 0 mod 13 and 24*n + 11 is squarefree. - _Robin Visser_, Jul 24 2023
%H A262542 Robin Visser, <a href="/A262542/b262542.txt">Table of n, a(n) for n = 1..5000</a>
%H A262542 Morris Newman, <a href="/A262308/a262308.pdf">Further identities and congruences for the coefficients of modular forms</a> [annotated scanned copy], Canadian J. Math 10 (1958): 577-586. See Table 1, column p=5.
%o A262542 (Sage)
%o A262542 for n in range(1, 1000):
%o A262542     p11 = product([(1 - x^k)^11 for k in range(1, n+1)])
%o A262542     p11n = int(p11.taylor(x, 0, n).coefficients()[n][0])
%o A262542     if (p11n%13 == 0) and (24*n + 11).is_squarefree():
%o A262542         print(n)  # _Robin Visser_, Jul 24 2023
%Y A262542 Cf. A010819.
%K A262542 nonn
%O A262542 1,1
%A A262542 _N. J. A. Sloane_, Oct 04 2015
%E A262542 More terms from _Robin Visser_, Jul 24 2023