A347088 a(n) = A055155(n) - d(n), where A055155(n) = Sum_{d|n} gcd(d, n/d) and d(n) gives the number of divisors of n.

0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 5, 0, 4, 0, 2, 0, 0, 0, 4, 4, 0, 4, 2, 0, 0, 0, 8, 0, 0, 0, 11, 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 10, 6, 8, 0, 2, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 4, 15, 0, 0, 0, 2, 0, 0, 0, 18, 0, 0, 8, 2, 0, 0, 0, 10, 12, 0, 0, 4, 0, 0, 0, 4, 0, 8, 0, 2, 0, 0, 0, 16, 0, 12, 4, 19, 0, 0, 0, 4, 0

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A055155(n) - A000005(n).

Prog

(PARI)
A055155(n) = sumdiv(n, d, gcd(d, n/d)); \\ From A055155
A347088(n) = (A055155(n)-numdiv(n));
(Python)
from sympy import gcd, divisors, divisor_count
def A347088(n): return sum(gcd(d, n//d) for d in divisors(n, generator=True)) - divisor_count(n) # Chai Wah Wu, Aug 19 2021

Crossrefs

Cf. A000005, A005117 (positions of zeros), A055155, A347089.

Sequence in context: A245254 A059080 A062070 * A343991 A239395 A182004

Adjacent sequences: A347085 A347086 A347087 * A347089 A347090 A347091

Keyword

nonn

Author

Antti Karttunen, Aug 17 2021

Status

approved