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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jul 15 2011
STATUS
approved