A247086 Integers k such that numerator and denominator of sigma(k)/k are both prime.

2, 12, 24, 90, 234, 528, 588, 1456, 4320, 4680, 9024, 11466, 26208, 35640, 55104, 55552, 90816, 114660, 121024, 123648, 185562, 199584, 297600, 510720, 674880, 2142720, 2190336, 4112640, 4316928, 5322240, 5659641, 7600320, 8714160, 10281600, 12999168, 15268368

Offset: 1

Author

Michel Marcus, Jan 10 2015

Keywords

• nonn

Comments

2 is the only squarefree term in this sequence. - Amiram Eldar, Jul 13 2024

Examples

			For k=2, sigma(k)/k = 3/2 with both numerator and denominator prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..114 (terms 1..69 from Michel Marcus)

Crossrefs

Cf. A000203 (sigma(n)).

Cf. A017665 (numerator of sigma(n)/n), A017666 (denominator of sigma(n)/n).

Programs

Mathematica

a247086Q[n_] := Block[{f = DivisorSigma[1, n]/n}, And[PrimeQ@ Numerator@ f, PrimeQ@ Denominator@ f]]; a247086[n_] := Select[Range@ n, a247086Q@ # &]; a247086[10^6] (* Michael De Vlieger, Jan 11 2015 *)

PARI

isok(n) = my(ab = sigma(n)/n); isprime(numerator(ab)) && isprime(denominator(ab));