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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). 7
 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 David A. Corneth, Table of n, a(n) for n = 1..2000 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 Cf. A000005, A000203, A046528, A286628, A289276. Sequence in context: A003260 A152058 A138865 * A145038 A138864 A105768 Adjacent sequences:  A051278 A051279 A051280 * A051282 A051283 A051284 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 September 21 02:29 EDT 2020. Contains 337266 sequences. (Running on oeis4.)