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A374290
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7-rough powerful numbers: numbers k coprime to 30 such that if a prime p divides k then p^2 also divides k.
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2
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1, 49, 121, 169, 289, 343, 361, 529, 841, 961, 1331, 1369, 1681, 1849, 2197, 2209, 2401, 2809, 3481, 3721, 4489, 4913, 5041, 5329, 5929, 6241, 6859, 6889, 7921, 8281, 9409, 10201, 10609, 11449, 11881, 12167, 12769, 14161, 14641, 16129, 16807, 17161, 17689, 18769
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OFFSET
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1,2
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COMMENTS
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This sequence is closed under multiplication.
The least term that is not a power of a prime (A000961) is a(25) = 7^2*11^2 = 5929.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = 80*zeta(2)*zeta(3)/(147*zeta(6)) = (80/147) * A082695 = 1.05773955745... .
In general, the sum of reciprocals of the p-rough powerful numbers is (zeta(2)*zeta(3)/zeta(6)) * Product_{prime q < p} ((q-1)*q/(q^2-q+1)).
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MATHEMATICA
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powQ[n_] := n == 1 || AllTrue[FactorInteger[n][[;; , 2]], # > 1 &]; Select[Range[20000], CoprimeQ[#, 30] && powQ[#] &]
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PROG
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(PARI) is(k) = gcd(k, 30) == 1 && ispowerful(k);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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