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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".
1
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 04 2015
EXTENSIONS
More terms from Robin Visser, Jul 24 2023
STATUS
approved