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A061680
a(n) = gcd(d(n^2), d(n)).
3
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 18 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Jul 26 2009
STATUS
approved