A219545 Integer values of sigma(n)/n that are prime.

2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 5, 5, 3, 2, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 7, 2, 5, 5, 7, 5, 5, 5, 7, 7, 7, 7, 5, 5, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 7, 7

Offset

1,1

Comments

Subsequence of A054030 consisting of primes among the abundancies sigma(m)/m of multiply perfect numbers m (see A007691).

Each 2 corresponds to a perfect number A000396, so if there are infinitely many perfect numbers, then the sequence is infinite.

If, in addition, there are only finitely many multiply perfect numbers m with sigma(m)/m > 2 (see A134639), then a(n) = 2 for all n > some N.

References

R. K. Guy, Unsolved Problems in Number Theory, B2.

Links

Table of n, a(n) for n=1..87.

A. Flammenkamp, The Multiply Perfect Numbers Page

Formula

a(n) = sigma(A065997(n))/A065997(n).

Example

A065997(1) = 6 and sigma(6)/6 = (1+2+3+6)/6 = 2, so a(1) = 2.

Mathematica

Select[Table[DivisorSigma[1, n]/n, {n, 10^6}], PrimeQ] (* The program only generates the first seven terms of the sequence. To generate them all, the value of n would have to be greatly increased. *) (* Harvey P. Dale, Oct 25 2021 *)

Crossrefs

Cf. A000396, A007691, A054030, A065997, A134639.

Sequence in context: A276856 A174296 A163178 * A029374 A255933 A340805

Adjacent sequences: A219542 A219543 A219544 * A219546 A219547 A219548

Keyword

nonn

Author

Jonathan Sondow, Nov 22 2012

Extensions

Extended by T. D. Noe, Nov 27 2012

Status

approved