A247222 Numbers n such that n = gcd(n^2, sigma(n^2)).

1, 39, 793, 7137, 76921, 863577, 2076867, 4317885, 8329831, 23402223, 53695813, 55871145, 224905437, 243762649, 1449786951, 2631094837, 2781581517, 3606816823, 6105766123, 6605555983, 6838433189, 8771312043, 13907907585, 35225161895, 42580779709, 56541691089

Offset: 1

Author

Michel Marcus, Nov 26 2014

Keywords

• nonn

Comments

Previous name was: Numbers n such that numerator(sigma(n^2)/n^2)*denominator(sigma(n^2)/n^2) = sigma(n^2).

That is, numbers n, such that A249670(n^2) = A000203(n^2).

Appears to be a subsequence of A232354.

Examples

			sigma(39^2)/39^2 = 61/39 = 2379 = sigma(39^2), so 39 is a term.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..48 (terms < 10^12)

Crossrefs

Cf. A000203, A249670, A249671.

Programs

Mathematica

Select[Range[10^6], GCD[#^2, DivisorSigma[1, #^2]] == # &] (* Giovanni Resta, Jun 10 2016 *)

PARI

isok(n) = {ab = sigma(n^2)/n^2; numerator(ab)*denominator(ab) == sigma(n^2);}

PARI

{isa(n) = if( n<1, 0, n == gcd(n^2, sigma(n^2)))}; /* Michael Somos, Nov 26 2014 */

Extensions

New name after Michael Somos by Michel Marcus, Nov 27 2014

a(13)-a(14) from Michel Marcus, Nov 27 2014

a(15)-a(26) from Giovanni Resta, Jun 10 2016