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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.)