A065997 Numbers n such that sigma(n) / n is prime.

6, 28, 120, 496, 672, 8128, 523776, 33550336, 459818240, 1476304896, 8589869056, 14182439040, 31998395520, 51001180160, 137438691328, 518666803200, 13661860101120, 30823866178560, 740344994887680, 796928461056000, 212517062615531520, 2305843008139952128

Offset: 1

Author

Joseph L. Pe, Dec 10 2001

Keywords

• nonn
• look

Comments

This is a subsequence of the sequence of multiply perfect numbers A007691.

The prime values of sigma(n) / n are A219545.

Numbers whose abundancy index is a prime. There are two visible bends (sudden changes in the growth rate) in the scatter plot. Compare also to the scatter plot of A336702. - Antti Karttunen, Feb 25 2022

Links

• Antti Karttunen, Table of n, a(n) for n = 1..597 (computed from the b-file of A007691 prepared by T. D. Noe, using Flammenkamp's data)

Crossrefs

Subsequence of A007691 and of A342924.

Cf. A000396, A005820, A046060 (subsequences).

Cf. A219545, A336702.

Programs

PARI

isA065997(n) = { my(p=sigma(n)/n); (1==denominator(p) && isprime(p)); }; \\ Antti Karttunen, Feb 25 2022

Extensions

Terms a(10) to a(14) from Jonathan Sondow, Nov 22 2012

Extended by T. D. Noe, Nov 26 2012