A347089 a(n) = gcd(A055155(n), d(n)), where A055155(n) = Sum_{d|n} gcd(d, n/d) and d(n) gives the number of divisors of n.

1, 2, 2, 1, 2, 4, 2, 2, 1, 4, 2, 2, 2, 4, 4, 5, 2, 2, 2, 2, 4, 4, 2, 4, 1, 4, 4, 2, 2, 8, 2, 2, 4, 4, 4, 1, 2, 4, 4, 4, 2, 8, 2, 2, 2, 4, 2, 10, 3, 2, 4, 2, 2, 8, 4, 4, 4, 4, 2, 4, 2, 4, 2, 1, 4, 8, 2, 2, 4, 8, 2, 6, 2, 4, 2, 2, 4, 8, 2, 10, 1, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 4, 2, 6, 2, 1, 2, 8, 2, 4, 8

Offset

1,2

Links

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

Formula

a(n) = gcd(A000005(n), A055155(n)).

a(n) = gcd(A000005(n), A347088(n)) = gcd(A055155(n), A347088(n)).

Prog

(PARI)
A055155(n) = sumdiv(n, d, gcd(d, n/d)); \\ From A055155
A347089(n) = gcd(A055155(n), numdiv(n));
(Python)
from sympy import gcd, divisors, divisor_count
def A347089(n): return gcd(divisor_count(n), sum(gcd(d, n//d) for d in divisors(n, generator=True))) # Chai Wah Wu, Aug 19 2021

Crossrefs

Cf. A000005, A055155, A347088.

Sequence in context: A069780 A369307 A366308 * A354825 A210531 A066954

Adjacent sequences: A347086 A347087 A347088 * A347090 A347091 A347092

Keyword

nonn

Author

Antti Karttunen, Aug 17 2021

Status

approved