A369564 - OEIS

A369564

Powerful numbers whose prime factors are all of the form 4*k + 3.

1, 9, 27, 49, 81, 121, 243, 343, 361, 441, 529, 729, 961, 1089, 1323, 1331, 1849, 2187, 2209, 2401, 3087, 3249, 3267, 3481, 3969, 4489, 4761, 5041, 5929, 6241, 6561, 6859, 6889, 8649, 9261, 9747, 9801, 10609, 11449, 11907, 11979, 12167, 14283, 14641, 16129, 16641

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Closed under multiplication.

LINKS

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

Index entries for sequences related to powerful numbers.

FORMULA

Sum_{n>=1} 1/a(n) = Product_{primes p == 3 (mod 4)} (1 + 1/(p*(p-1))) = 3*A013661*A334426/(4*A175647) = 1.2161513254... .

MATHEMATICA

q[n_] := n == 1 || AllTrue[FactorInteger[n], Mod[First[#], 4] == 3 && Last[#] > 1 &]; Select[Range[20000], q]