A347089 -id:A347089 - cp's OEIS frontend

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

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Antti Karttunen, Aug 17 2021

nonn

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

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

A055155(n) = sumdiv(n, d, gcd(d, n/d)); \\ From A055155
A347088(n) = (A055155(n)-numdiv(n));

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

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

cp's OEIS Frontend

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.

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