A056166 Numbers which are the product of distinct primes raised to prime powers.

1, 4, 8, 9, 25, 27, 32, 36, 49, 72, 100, 108, 121, 125, 128, 169, 196, 200, 216, 225, 243, 288, 289, 343, 361, 392, 441, 484, 500, 529, 675, 676, 800, 841, 864, 900, 961, 968, 972, 1000, 1089, 1125, 1152, 1156, 1225, 1323, 1331, 1352, 1369, 1372, 1444

Offset: 1

Author

Leroy Quet, Aug 01 2000

Keywords

• nonn

Examples

			200 is included because 200 = 2^3 * 5^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

Mathematica

{1}~Join~Select[Range[1500], AllTrue[FactorInteger[#][[All, -1]], PrimeQ] &] (* Michael De Vlieger, Aug 20 2017 *)

PARI

is(n)=#select(e->!isprime(e), factor(n)[,2])==0 \\ Charles R Greathouse IV, Sep 18 2015

Formula

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{q prime} 1/p^q) = 1.80728269690724154161... - Amiram Eldar, Oct 11 2020

Extensions

a(1) added, offset corrected by Charles R Greathouse IV, Sep 18 2015