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.

A062739 Odd powerful numbers.

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%I A062739 #32 Jan 08 2021 13:07:55
%S A062739 1,9,25,27,49,81,121,125,169,225,243,289,343,361,441,529,625,675,729,
%T A062739 841,961,1089,1125,1225,1323,1331,1369,1521,1681,1849,2025,2187,2197,
%U A062739 2209,2401,2601,2809,3025,3087,3125,3249,3267,3375,3481,3721,3969,4225
%N A062739 Odd powerful numbers.
%C A062739 Smallest term of this sequence not also in A075109 is 675, followed by 1125. - _Alonso del Arte_, Nov 22 2011
%D A062739 R. K. Guy, Unsolved Problems in Number Theory, B16
%H A062739 Zak Seidov, <a href="/A062739/b062739.txt">Table of n, a(n) for n = 1..10000</a>
%H A062739 W. A. Sentance, <a href="http://www.jstor.org/stable/2320553">Occurrences of consecutive odd powerful numbers</a>, Amer. Math. Monthly, 88 (1981), 272-274.
%F A062739 It is not true that a(n) = A001694(2n-1).
%F A062739 Sum_{n>=1} 1/a(n) = (2/3) * Sum_{n>=1} 1/A001694(n) = 2*zeta(2)*zeta(3)/(3*zeta(6)) = (2/3) * A082695 = 1.2957309... - _Amiram Eldar_, Jun 23 2020
%e A062739 Consecutive-odd examples from Sentance: {25,27},{70225,70227},{189750625,189750627}
%t A062739 Powerful[n_Integer] := (n ==1) || Min[Transpose[FactorInteger[n]][[2]]]>=2; Select[Range[5000],OddQ[ # ]&&Powerful[ # ]&] (* _T. D. Noe_, May 04 2006 *)
%t A062739 Join[{1},Select[Range[3,4301,2],Min[FactorInteger[#][[All,2]]]>1&]] (* _Harvey P. Dale_, Jan 08 2021 *)
%Y A062739 Cf. A001694, A060355, A060859, A060860, A082695.
%Y A062739 Cf. A076445 (consecutive odd powerful numbers).
%K A062739 nonn
%O A062739 1,2
%A A062739 _Labos Elemer_, Jul 12 2001
%E A062739 Checked by _T. D. Noe_, May 04 2006