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%I #20 Aug 18 2019 04:32:55
%S 9,25,289,729,1521,1681,2401,3481,5041,7921,10201,15625,17161,27889,
%T 28561,29929,83521,85849,146689,257049,279841,458329,491401,531441,
%U 552049,579121,597529,683929,703921,707281,734449,829921,1190281,1203409,1352569,1394761,1423249,1481089,1885129,2036329,2211169
%N Odd numbers N for which numerator(sigma(N)/N) is a prime.
%C This sequence includes all odd terms of A023194.
%C 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.
%C 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).
%C See A193066 for the square roots of the terms.
%C 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
%H Amiram Eldar, <a href="/A193065/b193065.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A193066(n)^2.
%t Select[Range[1,23*10^5,2],PrimeQ[Numerator[DivisorSigma[1,#]/#]]&] (* _Harvey P. Dale_, Sep 17 2017 *)
%o (PARI) forstep(N=1,1e7,2,isprime(numerator(sigma(N)/N)) && print1(N","))
%Y Cf. A000203.
%K nonn
%O 1,1
%A _M. F. Hasler_, Jul 15 2011
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