A353152 Perfect powers that are divisible by 5.

25, 100, 125, 225, 400, 625, 900, 1000, 1225, 1600, 2025, 2500, 3025, 3125, 3375, 3600, 4225, 4900, 5625, 6400, 7225, 8000, 8100, 9025, 10000, 11025, 12100, 13225, 14400, 15625, 16900, 18225, 19600, 21025, 22500, 24025, 25600, 27000, 27225, 28900, 30625

Offset

1,1

Comments

a(n) == 0 (mod 25).

a(n) == {0, 25, 75} (mod 100).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = (5*m)^k for some positive m and some k > 1. - David A. Corneth, Apr 28 2022

Sum_{n>=1} 1/a(n) = -Sum_{k>=2} mu(k)*zeta(k)/5^k = 0.0756933503... - Amiram Eldar, Jul 02 2022

Example

225 is a term since 225 = 15^2 is a power of a multiple of 5.

Mathematica

Select[Range[32000], And[GCD @@ FactorInteger[#][[All, 2]] > 1, Divisible[#, 5]] &] (* Michael De Vlieger, Apr 30 2022 *)

Prog

(PARI) isok(k) = ispower(k) && !(k%5); \\ Michel Marcus, Apr 27 2022
(PARI) upto(n) = { my(res = List()); forstep(i = 5, sqrtint(n), 5, c = i; for(e = 2, logint(n, i), c*=i; listput(res, c) ) ); Set(res) } \\ David A. Corneth, Apr 27 2022

Crossrefs

Cf. A000351, A011557.

Intersection of A001597 and A008587.

Cf. A075090 (even perfect powers).

Sequence in context: A158547 A144854 A237202 * A335717 A198385 A134422

Adjacent sequences: A353149 A353150 A353151 * A353153 A353154 A353155

Keyword

nonn,easy

Author

Marco Ripà, Apr 26 2022

Status

approved