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A247213
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Numbers n = Product_(p_i^e_i) such that nn = Product_((p_i + 2)^e_i) is divisible by n.
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1
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1, 2, 4, 8, 16, 32, 64, 105, 128, 210, 256, 315, 420, 512, 630, 840, 1024, 1260, 1575, 1680, 2048, 2520, 3150, 3360, 4096, 5040, 6300, 6720, 8192, 10080, 11025, 12600, 13440, 16384, 20160, 22050, 25200, 26880, 32768, 33075, 40320, 44100, 50400, 53760, 65536
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OFFSET
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1,2
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COMMENTS
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That is, numbers n, such that A166590(n) is divisible by n.
A000079, powers of 2, is a subsequence.
Thomas Ordowski remarks that the only squarefrees of this sequence are: 1, 2, 105, and 210.
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LINKS
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EXAMPLE
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A166590(2)=4 is divisible by 2, so 2 is in the sequence.
A166590(105) = A166590(3*5*7) = 5*7*9 = 3*(3*5*7), so 105 is in the sequence.
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MATHEMATICA
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a247213[n_] := Select[Range@n, Mod[Times @@ Power @@@ Transpose[{Plus[First /@ FactorInteger@#, 2], Last /@ FactorInteger@#}], #] == 0 &]; a247213[2^16] (* Michael De Vlieger, Jan 07 2015 *)
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PROG
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(PARI) isok(n) = { f = factor(n); for (i=1, #f~, f[i, 1] += 2); newn = factorback(f); newn % n == 0; }
(Python)
from operator import mul
from functools import reduce
from sympy import factorint
A247213_list = [n for n in range(1, 10**4) if n <= 1 or not reduce(mul, [(p+2)**e for p, e in factorint(n).items()]) % n]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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