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

1,2

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A158340 A350014 A259183 * A093771 A371223 A051676

Adjacent sequences: A056163 A056164 A056165 * A056167 A056168 A056169

Keyword

nonn

Author

Leroy Quet, Aug 01 2000

Extensions

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

Status

approved