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A369566
Powerful numbers whose prime factors are all of the form 3*k + 2.
4
1, 4, 8, 16, 25, 32, 64, 100, 121, 125, 128, 200, 256, 289, 400, 484, 500, 512, 529, 625, 800, 841, 968, 1000, 1024, 1156, 1331, 1600, 1681, 1936, 2000, 2048, 2116, 2209, 2312, 2500, 2809, 3025, 3125, 3200, 3364, 3481, 3872, 4000, 4096, 4232, 4624, 4913, 5000
OFFSET
1,2
COMMENTS
Closed under multiplication.
FORMULA
Sum_{n>=1} 1/a(n) = Product_{primes p == 2 (mod 3)} (1 + 1/(p*(p-1))) = (9/8) * A333240 * A334479 = 1.6053538210...
MATHEMATICA
q[n_] := n == 1 || AllTrue[FactorInteger[n], Mod[First[#], 3] == 2 && Last[#] > 1 &]; Select[Range[5000], q]
PROG
(PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 1]%3 != 2 || f[i, 2] == 1, return(0))); 1; }
CROSSREFS
Intersection of A001694 and A004612.
Similar sequence: A352492, A369563, A369564, A369565.
Sequence in context: A330992 A246067 A161226 * A022560 A290190 A193452
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 26 2024
STATUS
approved