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A071114
Numbers n such that n and sigma(n) are prime powers (of the form p^k, p prime, k>=1).
2
2, 3, 4, 7, 9, 16, 25, 31, 64, 81, 127, 289, 729, 1681, 2401, 3481, 4096, 5041, 7921, 8191, 10201, 15625, 17161, 27889, 28561, 29929, 65536, 83521, 85849, 131071, 146689, 262144, 279841, 458329, 491401, 524287, 531441, 552049, 579121, 597529
OFFSET
1,1
COMMENTS
Includes (m+1)/2 for m in A000668. By Mihailescu's theorem, these are the only powers of 2 in the sequence. - Robert Israel, Feb 09 2017
LINKS
MAPLE
pp:= n -> nops(ifactors(n)[2])=1:
select(n-> pp(n) and pp(numtheory:-sigma(n)), [$1..10^6]); # Robert Israel, Feb 09 2017
MATHEMATICA
Select[Range[600000], PrimePowerQ[#] && PrimePowerQ[DivisorSigma[1, #]] &] (* Ivan Neretin, Feb 08 2017 *)
PROG
(PARI) for(n=1, 100000, if(omega(n)*omega(sigma(n)) == 1, print1(n, ", ")))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 27 2002
EXTENSIONS
Edited by Robert G. Wilson v and David Wasserman, May 30 2002
STATUS
approved