A364558 a(n) = A364557(n) - A000010(n), where A364557 is the Möbius transform of A005941, and A000010 (Euler phi) is the Möbius transform of A000027.

0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 6, 0, 20, 2, -4, 0, 48, -2, 110, 0, -4, 6, 234, 0, -12, 20, -10, 4, 484, -4, 994, 0, -4, 48, -16, -4, 2012, 110, 8, 0, 4056, -4, 8150, 12, -16, 234, 16338, 0, -26, -12, 32, 40, 32716, -10, -24, 8, 92, 484, 65478, -8, 131012, 994, -20, 0, -16, -4, 262078, 96, 212, -16, 524218, -8, 1048504

Offset

1,7

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Prog

(PARI) A364558(n) = (A364557(n)-eulerphi(n));
(Python)
from math import prod
from sympy import factorint, primepi
def A364558(n): return (1<<primepi(max(f:=factorint(n)))+sum(e-1 for e in f.values())-1)-prod(p**(e-1)*(p-1) for p, e in f.items()) if n>1 else 0 # Chai Wah Wu, Jul 29 2023

Crossrefs

Cf. A000010, A005941, A364557, A364559 (inverse Möbius transform), A364565 (positions of 0's), A364566 (of terms < 0).

Sequence in context: A158327 A368707 A136581 * A364559 A354607 A175950

Adjacent sequences: A364555 A364556 A364557 * A364559 A364560 A364561

Keyword

sign

Author

Antti Karttunen, Jul 28 2023

Status

approved