# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a062739 Showing 1-1 of 1 %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, Table of n, a(n) for n = 1..10000 %H A062739 W. A. Sentance, Occurrences of consecutive odd powerful numbers, 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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE