A330574 a(n) = r_2(n)^2*d(n+1), where r_2 = A004018, d = A000005.

1, 32, 32, 0, 32, 256, 0, 0, 48, 64, 128, 0, 0, 256, 0, 0, 32, 384, 32, 0, 256, 0, 0, 0, 0, 576, 256, 0, 0, 512, 0, 0, 64, 0, 256, 0, 32, 256, 0, 0, 128, 512, 0, 0, 0, 256, 0, 0, 0, 96, 576, 0, 128, 512, 0, 0, 0, 0, 128, 0, 0, 256, 0, 0, 64, 2048, 0, 0, 256, 0, 0, 0, 32, 256, 384, 0, 0, 0, 0, 0, 320, 64, 128, 0, 0

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Karl-Heinz Indlekofer, Eine asymptotische Formel in der Zahlentheorie, (German) Arch. Math. (Basel) 23 (1972), 619-624. MR0318080 (47 #6629).

Mathematica

Table[SquaresR[2, n]^2 * DivisorSigma[0, n+1], {n, 0, 100}] (* Amiram Eldar, Mar 05 2020 *)

Prog

(Python)
from math import prod
from sympy import factorint
def A330574(n): return prod(1 if p==2 else (e+1 if p&3==1 else (e+1)&1) for p, e in factorint(n).items())**2*prod(e+1 for e in factorint(n+1).values())<<4 if n else 1 # Chai Wah Wu, May 29 2026

Crossrefs

Cf. A000005, A004018, A331071.

Sequence in context: A023474 A131762 A208129 * A126271 A010871 A248767

Adjacent sequences: A330571 A330572 A330573 * A330575 A330576 A330577

Keyword

nonn,changed

Author

N. J. A. Sloane, Jan 10 2020

Extensions

Offset corrected by Amiram Eldar, Mar 05 2020

Status

approved