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A065997 Numbers n such that sigma(n) / n is prime. 8
6, 28, 120, 496, 672, 8128, 523776, 33550336, 459818240, 1476304896, 8589869056, 14182439040, 31998395520, 51001180160, 137438691328, 518666803200, 13661860101120, 30823866178560, 740344994887680, 796928461056000, 212517062615531520, 2305843008139952128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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)

PROG

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

CROSSREFS

Subsequence of A007691 and of A342924.

Cf. A000396, A005820, A046060 (subsequences).

Cf. A219545, A336702.

Sequence in context: A348031 A260508 A334410 * A348035 A354073 A006516

Adjacent sequences:  A065994 A065995 A065996 * A065998 A065999 A066000

KEYWORD

nonn,look

AUTHOR

Joseph L. Pe, Dec 10 2001

EXTENSIONS

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

Extended by T. D. Noe, Nov 26 2012

STATUS

approved

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Last modified September 27 19:17 EDT 2022. Contains 357062 sequences. (Running on oeis4.)