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 A278911 Odd numbers with prime sum of divisors. 3
 9, 25, 289, 729, 1681, 2401, 3481, 5041, 7921, 10201, 15625, 17161, 27889, 28561, 29929, 83521, 85849, 146689, 279841, 458329, 491401, 531441, 552049, 579121, 597529, 683929, 703921, 707281, 734449, 829921, 1190281, 1203409, 1352569, 1394761, 1423249, 1481089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also odd numbers with prime number and sum of divisors; if the sum of divisors is prime, then the number of divisors is prime. Values of prime sums are sorted in A247837. Subsequence of A050150 (odd numbers with prime number of divisors). Odd terms of A023194. All terms are squares of the form p^e such that p is odd prime and e+1 is a prime. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A193070(n)^2. - Michel Marcus, Dec 01 2016 EXAMPLE sigma(9) = 13 (prime). MAPLE N:= 10^7: # to get all terms <= N Ps:= select(isprime, [seq(i, i=3..floor(N^(1/2)), 2)]): es:= map(`-`, select(isprime, [seq(i, i=3..floor(log[3](N))+1, 2)]), 1): Pes:= [seq(seq([p, e], p=Ps), e=es)]: filter:= proc(pe) local v; v:= (pe[1]^(pe[2]+1)-1)/(pe[1]-1); pe[1]^pe[2] <= N and isprime(v) end proc: sort(map(pe -> pe[1]^pe[2], select(filter, Pes))); # Robert Israel, Jan 22 2019 MATHEMATICA Select[Range[1, 2*10^6, 2], PrimeQ@DivisorSigma[1, #] &] (* Michael De Vlieger, Dec 01 2016 *) PROG (MAGMA) [n: n in[2..10^7] | IsOdd(n) and IsPrime(SumOfDivisors(n)) and IsPrime(NumberOfDivisors(n))] (PARI) isok(n) = (n % 2) && isprime(sigma(n)); \\ Michel Marcus, Dec 01 2016 CROSSREFS Cf. A000203, A005408, A023194, A050150, A193070, A247837, A278914. Sequence in context: A293720 A227891 A193065 * A201807 A228465 A048056 Adjacent sequences:  A278908 A278909 A278910 * A278912 A278913 A278914 KEYWORD nonn AUTHOR Jaroslav Krizek, Nov 30 2016 STATUS approved

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Last modified October 22 18:08 EDT 2019. Contains 328319 sequences. (Running on oeis4.)