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A247086
Integers k such that numerator and denominator of sigma(k)/k are both prime.
3
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Jan 10 2015
STATUS
approved