A348968 a(n) = gcd(n, A099377(n)), where A099377(n) is the numerator of the harmonic mean of the divisors of n.

1, 2, 3, 4, 5, 2, 7, 8, 9, 10, 11, 6, 13, 7, 5, 16, 17, 18, 19, 20, 21, 22, 23, 8, 25, 26, 27, 1, 29, 10, 31, 32, 11, 34, 35, 36, 37, 38, 39, 8, 41, 7, 43, 22, 45, 23, 47, 24, 49, 50, 17, 52, 53, 18, 55, 56, 57, 58, 59, 30, 61, 31, 63, 64, 65, 11, 67, 68, 23, 35, 71, 72, 73, 74, 75, 38, 77, 26, 79, 80, 81, 82, 83, 3

Offset: 1

Author

Antti Karttunen, Nov 05 2021

Keywords

• nonn

Crossrefs

Cf. A057021, A099377, A348510, A348969.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A099377(n) = { my(d=divisors(n)); numerator(#d/sum(k=1, #d, 1/d[k])); }; \\ From A099377
A348968(n) = gcd(n, A099377(n));

Formula

a(n) = gcd(n, A099377(n)) = gcd(n, A348510(n)) = gcd(A099377(n), A348510(n)).

a(n) = n / A348969(n).

a(n) = A099377(n) / A057021(n). [Apparently, holds at least up to n = 2^25]