OFFSET
1,1
COMMENTS
All terms are square. Moreover, each term is of the form p^j where both p and j*3 + 1 are prime (see A279094).
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
EXAMPLE
4 is in the sequence because sigma(4^3) = sigma(2^6) = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127, which is prime.
16 is in the sequence because sigma(16^3) = sigma(2^12) = Sum_{m=0..12} 2^m = (2^13 - 1)/(2 - 1) = 8191, which is prime.
36 is not in the sequence because sigma(36^3) = sigma(2^6*3^6) = ((2^7 - 1)/(2 - 1))*((3^7 - 1)/(3 - 1)) = 127*1093, which is not prime. (36 is not of the form p^j where p is prime.)
361 is not in the sequence (even though 361 = 19^2 is of the form p^j where both p and 3*j + 1 are prime) because sigma(361^3) = sigma(19^6) = (19^7 - 1)/(19 - 1) = 49659541 = 701 * 70841.
MATHEMATICA
mx = 10^7; ee = Select[Range@ Log2@ mx, PrimeQ[3 # + 1] &]; Union@ Reap[ Do[ Do[ If[(v = p^e) <= mx, If[ PrimeQ[(p v^3 - 1)/ (p-1)], Sow@ v], Break[]], {e, ee}], {p, Prime@ Range@ PrimePi@ Sqrt@ mx}]][[2, 1]] (* Giovanni Resta, Mar 12 2017 *)
Select[Range[2*10^6], PrimeQ[DivisorSigma[1, #^3]]&] (* Harvey P. Dale, Jan 10 2024 *)
PROG
(PARI) isok(n) = isprime(sigma(n^3)); \\ Michel Marcus, Mar 12 2017
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Jon E. Schoenfield, Mar 12 2017
STATUS
approved