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

1,1

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.

Prog

(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

Crossrefs

Cf. A010819.

Sequence in context: A090991 A019533 A053301 * A315351 A315352 A315353

Adjacent sequences: A262539 A262540 A262541 * A262543 A262544 A262545

Keyword

nonn

Author

N. J. A. Sloane, Oct 04 2015

Extensions

More terms from Robin Visser, Jul 24 2023

Status

approved