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.

A322797 Powerful tau numbers.

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%I A322797 #47 Dec 30 2019 10:06:23
%S A322797 1,8,9,36,72,108,128,225,288,441,625,864,972,1089,1152,1521,1800,1944,
%T A322797 2000,2025,2601,2700,3249,3456,3528,3600,4500,4761,5000,5292,5625,
%U A322797 6561,6912,7569,7776,8100,8649,8712,10000,10800,12168,12321,12348,13068,15129,16000,16200,16641,18000
%N A322797 Powerful tau numbers.
%C A322797 If the largest exponent among the prime factors of a(n) does not exceed 2 then A046692(a(n)) = sqrt(a(n)), otherwise A046692(a(n)) = 0.
%H A322797 Amiram Eldar, <a href="/A322797/b322797.txt">Table of n, a(n) for n = 1..10000</a>
%e A322797 1 is a term because A033950(1) = A001694(1) = 1.
%e A322797 8 is a term because A033950(8) divides A001694(3).
%e A322797 9 is a term because A033950(9) divides A001694(4).
%e A322797 36 is a term because A033950(36) divides A001694(9).
%t A322797 powtauQ[1] = True; powtauQ[n_] := Min[e = (Last /@ FactorInteger[n])] > 1 && Divisible[n, Times @@ (e + 1)]; Select[Range[18000], powtauQ] (* _Amiram Eldar_, Dec 30 2019 *)
%o A322797 (PARI) isok(n) = ispowerful(n) && ((n % numdiv(n)) == 0); \\ _Michel Marcus_, Jan 16 2019
%Y A322797 Intersection of A001694 (powerful numbers) and A033950 (tau numbers).
%Y A322797 Cf. A001494, A033950, A046692.
%K A322797 nonn
%O A322797 1,2
%A A322797 _Torlach Rush_, Jan 10 2019
%E A322797 Corrected and extended by _Michel Marcus_, Jan 16 2019