cp's OEIS Frontend

A278911 Odd numbers with prime sum of divisors.

%I A278911 #19 Jul 20 2025 13:17:45
%S A278911 9,25,289,729,1681,2401,3481,5041,7921,10201,15625,17161,27889,28561,
%T A278911 29929,83521,85849,146689,279841,458329,491401,531441,552049,579121,
%U A278911 597529,683929,703921,707281,734449,829921,1190281,1203409,1352569,1394761,1423249,1481089
%N A278911 Odd numbers with prime sum of divisors.
%C A278911 Also odd numbers with prime number and sum of divisors; if the sum of divisors is prime, then the number of divisors is prime.
%C A278911 Values of prime sums are sorted in A247837.
%C A278911 Subsequence of A050150 (odd numbers with prime number of divisors).
%C A278911 Odd terms of A023194.
%C A278911 All terms are squares of the form p^e such that p is odd prime and e+1 is a prime.
%H A278911 Robert Israel, <a href="/A278911/b278911.txt">Table of n, a(n) for n = 1..10000</a>
%F A278911 a(n) = A193070(n)^2. - _Michel Marcus_, Dec 01 2016
%e A278911 sigma(9) = 13 (prime).
%p A278911 N:= 10^7: # to get all terms <= N
%p A278911 Ps:= select(isprime, [seq(i,i=3..floor(N^(1/2)),2)]):
%p A278911 es:= map(`-`,select(isprime, [seq(i,i=3..floor(log[3](N))+1,2)]),1):
%p A278911 Pes:= [seq(seq([p,e],p=Ps),e=es)]:
%p A278911 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:
%p A278911 sort(map(pe -> pe[1]^pe[2], select(filter, Pes))); # _Robert Israel_, Jan 22 2019
%t A278911 Select[Range[1, 2*10^6, 2], PrimeQ@DivisorSigma[1, #] &] (* _Michael De Vlieger_, Dec 01 2016 *)
%o A278911 (Magma) [n: n in[2..10^7] | IsOdd(n) and IsPrime(SumOfDivisors(n)) and IsPrime(NumberOfDivisors(n))];
%o A278911 (PARI) isok(n) = (n % 2) && isprime(sigma(n)); \\ _Michel Marcus_, Dec 01 2016
%Y A278911 Cf. A000203, A005408, A023194, A050150, A193070, A247837, A278914.
%K A278911 nonn
%O A278911 1,1
%A A278911 _Jaroslav Krizek_, Nov 30 2016