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A278911
Odd numbers with prime sum of divisors.
4
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
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
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Nov 30 2016
STATUS
approved