A065997 - OEIS

%I #25 Feb 25 2022 10:31:57

%S 6,28,120,496,672,8128,523776,33550336,459818240,1476304896,

%T 8589869056,14182439040,31998395520,51001180160,137438691328,

%U 518666803200,13661860101120,30823866178560,740344994887680,796928461056000,212517062615531520,2305843008139952128

%N Numbers n such that sigma(n) / n is prime.

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

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

%C 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

%H Antti Karttunen, <a href="/A065997/b065997.txt">Table of n, a(n) for n = 1..597</a> (computed from the b-file of A007691 prepared by T. D. Noe, using Flammenkamp's data)

%o (PARI) isA065997(n) = { my(p=sigma(n)/n); (1==denominator(p) && isprime(p)); }; \\ _Antti Karttunen_, Feb 25 2022

%Y Subsequence of A007691 and of A342924.

%Y Cf. A000396, A005820, A046060 (subsequences).

%Y Cf. A219545, A336702.

%K nonn,look

%O 1,1

%A _Joseph L. Pe_, Dec 10 2001

%E Terms a(10) to a(14) from _Jonathan Sondow_, Nov 22 2012

%E Extended by _T. D. Noe_, Nov 26 2012