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A051281
Sum of divisors of n, sigma(n) (A000203), is a power of number of divisors of n, d(n) (A000005).
13
1, 3, 7, 31, 127, 217, 889, 2667, 3937, 8191, 27559, 57337, 131071, 172011, 253921, 524287, 917497, 1040257, 1777447, 3670009, 4063201, 11010027, 12189603, 16252897, 16646017, 66584449, 113770279, 116522119, 225735769, 677207307, 1073602561, 2147483647, 3612185689, 4294434817, 7515217927
OFFSET
1,2
COMMENTS
All Mersenne primes (A000668) are terms.
Subsequence of A046528 (product of distinct Mersenne primes). - Michel Marcus, Feb 15 2020
LINKS
EXAMPLE
d(217) = 4; sigma(217) = 256 = 4^4.
MATHEMATICA
spdQ[n_]:=Module[{sd=DivisorSigma[1, n], nd=DivisorSigma[0, n]}, sd == nd^IntegerExponent[sd, nd]]; Join[{1}, Select[Range[2, 226000000], spdQ]] (* Harvey P. Dale, May 02 2012 *)
PROG
(PARI) is(n)=my(t, e=ispower(sigma(n), , &t)); if(!e, return(n==1), nd); nd=numdiv(n); fordiv(e, d, if(t^d==nd, return(1))); 0 \\ Charles R Greathouse IV, Feb 19 2013
(PARI) isA051281(n) = { if(n==1, return(1)); my(sig = sigma(n), ndiv = numdiv(n), v = valuation(sig, ndiv)); (ndiv^v == sig); } \\ Antti Karttunen, Jun 30 2017
CROSSREFS
KEYWORD
nonn,nice
EXTENSIONS
More terms from Jud McCranie
a(30)-a(32) from Donovan Johnson, Oct 03 2012
a(33)-a(35) from Michel Marcus, Feb 14 2020
STATUS
approved