A347088 - OEIS

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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.

2

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

(list; graph; refs; listen; history; text; internal format)

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