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

6, 10, 17, 18, 24, 27, 57, 68, 69, 74, 90, 95, 98, 103, 123, 127, 131, 163, 179, 197, 204, 210, 238, 239, 249, 250, 253, 256, 258, 259, 270, 274, 278, 282, 292, 326, 349, 359, 360, 364, 373, 374, 376, 378, 400, 407, 424, 425, 447, 448, 451, 454, 474, 480, 492, 493, 507, 558, 563, 569

Offset: 1

Author

N. J. A. Sloane, Oct 04 2015

Keywords

• nonn

Comments

These are exactly the numbers n such that A010819(n) = 0 mod 13 and 24*n + 11 is squarefree. - Robin Visser, Jul 24 2023

Links

• Robin Visser, Table of n, a(n) for n = 1..5000
• Morris Newman, Further identities and congruences for the coefficients of modular forms [annotated scanned copy], Canadian J. Math 10 (1958): 577-586. See Table 1, column p=5.

Crossrefs

Cf. A010819.

Programs

Sage

for n in range(1, 1000):
    p11 = product([(1 - x^k)^11 for k in range(1, n+1)])
    p11n = int(p11.taylor(x, 0, n).coefficients()[n][0])
    if (p11n%13 == 0) and (24*n + 11).is_squarefree():
        print(n)  # Robin Visser, Jul 24 2023

Extensions

More terms from Robin Visser, Jul 24 2023