cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A219338 Numbers n for which n = (tau(n) - 1)^k with integer k.

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%I A219338 #17 Nov 19 2012 12:35:41
%S A219338 4,16,27,3125,3375,65536,823543,3748096,52521875,285311670611,
%T A219338 7625597484987,302875106592253,1156831381426176,66182427701415936,
%U A219338 827240261886336764177,511324276025564512546607,1978419655660313589123979,281633339785852578930098176
%N A219338 Numbers n for which n = (tau(n) - 1)^k with integer k.
%C A219338 tau(n) is the number of positive divisors of n.
%F A219338 Numbers n for which n = (tau(n) - 1)^k with integer k.
%e A219338 a(1) = 4 because (tau(4) - 1)^2 = (3 - 1)^2 = 4 and this is the first number satisfying this condition.
%e A219338 a(2) = 16 because (tau(16) - 1)^2 = (5 - 1)^2 = 16 and this is the second number satisfying this condition.
%e A219338 a(3) = 27 because (tau(27) - 1)^3 = (4 - 1)^3 = 27 and this is the third number satisfying this condition.
%t A219338 Select[Range[10^4], IntegerQ[Log[DivisorSigma[0, #] - 1, #]] &] (* _Alonso del Arte_, Nov 18 2012 *)
%o A219338 (PARI) v=vector(18); mx=3*10^26; c=0; for(m=2, 3440639, for(k=2, 87, n=m^k; if(n>mx, next(2)); if(m==numdiv(n)-1, c++; v[c]=n))); v=vecsort(v); for(i=1, c, print1(v[i]", ")) /* _Donovan Johnson_, Nov 19 2012 */
%Y A219338 Cf. A180936.
%K A219338 nonn
%O A219338 1,1
%A A219338 _Zdenek Cervenka_, Nov 18 2012
%E A219338 a(10)-a(18) from _Donovan Johnson_, Nov 19 2012