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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A003260 A152058 A138865 * A145038 A354536 A138864
KEYWORD
nonn,nice
AUTHOR
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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)