A363190 Odd powerful numbers (A062739) k such that the next powerful number after k is also odd.

25, 121, 225, 343, 1089, 1323, 2187, 2197, 3025, 3087, 3249, 5929, 6125, 6859, 7803, 8575, 9261, 10125, 11881, 11907, 14161, 15125, 16641, 16807, 19683, 19773, 21025, 22707, 25921, 27889, 29241, 29791, 30375, 33275, 36125, 41067, 42849, 44217, 45125, 45369, 49729

Offset

1,1

Comments

A076445 is a subsequence if there are no three consecutive integers that are powerful numbers (A001694).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

25 = 5^2 is a term since it is an odd powerful number and the next powerful number, 27 = 3^3, is also odd.

Mathematica

With[{pow = Select[Range[10^5], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]}, pow[[Select[Range[Length[pow] - 1], OddQ[pow[[#]]] && OddQ[pow[[#+1]]] &]]]]

Prog

(PARI) lista(kmax) = {my(c = 0); for(k = 1, kmax, if(ispowerful(k), c++; if(k%2, print1(c, ", ")))); }

Crossrefs

Cf. A001694, A062739, A076445, A363189, A363191, A363192.

Sequence in context: A256519 A298009 A213445 * A031151 A016970 A174371

Adjacent sequences: A363187 A363188 A363189 * A363191 A363192 A363193

Keyword

nonn,easy

Author

Amiram Eldar, May 21 2023

Status

approved