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A219545 Integer values of sigma(n)/n that are prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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.

CROSSREFS

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

Sequence in context: A276856 A174296 A163178 * A029374 A255933 A319396

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

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Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)