A193065 Odd numbers N for which numerator(sigma(N)/N) is a prime.

9, 25, 289, 729, 1521, 1681, 2401, 3481, 5041, 7921, 10201, 15625, 17161, 27889, 28561, 29929, 83521, 85849, 146689, 257049, 279841, 458329, 491401, 531441, 552049, 579121, 597529, 683929, 703921, 707281, 734449, 829921, 1190281, 1203409, 1352569, 1394761, 1423249, 1481089, 1885129, 2036329, 2211169

Offset

1,1

Comments

This sequence includes all odd terms of A023194.

For most of the terms, sigma(N) is prime (i.e., N is in A023194); the first two exceptions are sigma(a(5))=3*13*61 and sigma(a(20))=13*30941. See A193072 for (the square root of) these exceptions.

It is well known that sigma(N) can't be odd unless N is a square (since sigma is multiplicative and sigma(p^e)=1+...+p^e) or twice a square (excluded here).

See A193066 for the square roots of the terms.

The sequence of numbers n for which A002129(n) is prime starts as this sequence here, but excludes a(5), a(20) etc. - R. J. Mathar, Sep 18 2011

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Formula

a(n) = A193066(n)^2.

Mathematica

Select[Range[1, 23*10^5, 2], PrimeQ[Numerator[DivisorSigma[1, #]/#]]&] (* Harvey P. Dale, Sep 17 2017 *)

Prog

(PARI) forstep(N=1, 1e7, 2, isprime(numerator(sigma(N)/N)) && print1(N", "))

Crossrefs

Cf. A000203.

Sequence in context: A013397 A293720 A227891 * A278911 A330828 A201807

Adjacent sequences: A193062 A193063 A193064 * A193066 A193067 A193068

Keyword

nonn

Author

M. F. Hasler, Jul 15 2011

Status

approved