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A193065 Odd numbers N for which numerator(sigma(N)/N) is a prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..41.

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 A201807 A228465

Adjacent sequences:  A193062 A193063 A193064 * A193066 A193067 A193068

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jul 15 2011

STATUS

approved

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Last modified February 19 12:48 EST 2018. Contains 299333 sequences. (Running on oeis4.)