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

1,2

Links

Table of n, a(n) for n=1..84.

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]

Prog

(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));

Crossrefs

Cf. A057021, A099377, A348510, A348969.

Sequence in context: A344758 A053626 A348990 * A333696 A134364 A338579

Adjacent sequences: A348965 A348966 A348967 * A348969 A348970 A348971

Keyword

nonn

Author

Antti Karttunen, Nov 05 2021

Status

approved