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

Author

Amiram Eldar, May 21 2023

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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