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A051281
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Sum of divisors of n, sigma(n) (A000203), is a power of number of divisors of n, d(n) (A000005).
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13
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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
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OFFSET
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1,2
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COMMENTS
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All Mersenne primes (A000668) are terms.
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LINKS
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EXAMPLE
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d(217) = 4; sigma(217) = 256 = 4^4.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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