A061680 a(n) = gcd(d(n^2), d(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 3, 1, 1, 1, 1, 1, 1

Offset

1,12

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Harry J. Smith)

Formula

a(n) = gcd(A000005(A000290(n)), A000005(n)) = gcd(A048691(n), A000005(n)).

Example

This GCD can only be odd since d(n^2) is odd.
For n = 4608: a(4608) = gcd(d(21233664), d(4608)) = gcd(95, 30) = 5.

Mathematica

Table[GCD[DivisorSigma[0, n], DivisorSigma[0, n^2]], {n, 110}] (* Harvey P. Dale, Sep 03 2023 *)

Prog

(PARI) a(n) = gcd(numdiv(n^2), numdiv(n)); \\ Harry J. Smith, Jul 26 2009
(PARI) a(n) = {my(e = factor(n)[, 2]); gcd(vecprod(apply(x -> 2*x+1, e)), vecprod(apply(x -> x+1, e))); } \\ Amiram Eldar, Dec 02 2023

Crossrefs

Cf. A000005, A000290, A048691.

Sequence in context: A322361 A219208 A336850 * A355456 A097558 A124385

Adjacent sequences: A061677 A061678 A061679 * A061681 A061682 A061683

Keyword

nonn

Author

Labos Elemer, Jun 18 2001

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Jul 26 2009

Status

approved