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A306458
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a(n) = A001694(n)/A007947(A001694(n)), the powerful numbers divided by their squarefree kernel.
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4
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1, 2, 4, 3, 8, 5, 9, 16, 6, 7, 32, 12, 27, 10, 18, 11, 25, 64, 24, 13, 14, 20, 36, 15, 81, 128, 48, 17, 54, 49, 19, 28, 40, 72, 21, 22, 50, 256, 23, 96, 125, 108, 45, 26, 243, 56, 80, 29, 144, 30, 31, 44, 162, 100, 512, 33, 75, 192, 34, 35, 216, 63, 121, 52
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OFFSET
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1,2
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COMMENTS
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A permutation of the positive integers.
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LINKS
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FORMULA
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MAPLE
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N:= 10^4: # to get terms corresponding to powerful numbers <= N
rad:= n -> convert(numtheory:-factorset(n), `*`):
S:= {1}:
p:= 1:
do
p:= nextprime(p);
if p^2 > N then break fi;
S:= S union map(t -> seq(t*p^i, i=2..floor(log[p](N/t))), select(`<=`, S, N/p^2));
od:
map(t -> t/rad(t), sort(convert(S, list))); # Robert Israel, Mar 20 2019
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MATHEMATICA
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PROG
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(PARI) apply(x->(x/factorback(factorint(x)[, 1])), select(x->ispowerful(x), vector(1600, k, k))) \\ Michel Marcus, Feb 17 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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