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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000203 (sigma(n)).

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

Sequence in context: A176679 A278407 A224923 * A337077 A121119 A226899

Adjacent sequences: A247083 A247084 A247085 * A247087 A247088 A247089

Keyword

nonn

Author

Michel Marcus, Jan 10 2015

Status

approved