A330691 a(n) = gcd(n, A309639(n)), where A309639(n) is the index of the least harmonic number H_i whose denominator (A002805) is divisible by n.

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 4, 13, 7, 5, 16, 17, 9, 19, 5, 3, 11, 23, 3, 25, 13, 27, 7, 29, 5, 31, 32, 11, 17, 7, 9, 37, 19, 13, 8, 41, 3, 43, 11, 9, 23, 47, 16, 49, 25, 17, 13, 53, 27, 11, 8, 19, 29, 59, 5, 61, 31, 9, 64, 13, 11, 67, 17, 3, 7, 71, 9, 73, 37, 25, 19, 11, 13, 79, 16, 81, 41, 83, 3, 17, 43, 29, 11, 89, 9

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = gcd(n, A309639(n)).

a(n) = n/A330692(n).

Mathematica

A309639[n_] := For[k = 1, True, k++, If[Divisible[Denominator[ HarmonicNumber[k]], n], Return[k]]];
a[n_] := GCD[n, A309639[n]];
Array[a, 105]

Prog

(PARI) A330691(n) = gcd(n, A309639(n));

Crossrefs

Cf. A000961 (fixed points).

Cf. A002805, A309639, A330692, A330742.

Sequence in context: A098988 A274346 A345993 * A034699 A354933 A346596

Adjacent sequences: A330688 A330689 A330690 * A330692 A330693 A330694

Keyword

nonn

Author

Antti Karttunen, Dec 29 2019

Status

approved