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A166590
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Totally multiplicative sequence with a(p) = p+2 for prime p.
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22
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1, 4, 5, 16, 7, 20, 9, 64, 25, 28, 13, 80, 15, 36, 35, 256, 19, 100, 21, 112, 45, 52, 25, 320, 49, 60, 125, 144, 31, 140, 33, 1024, 65, 76, 63, 400, 39, 84, 75, 448, 43, 180, 45, 208, 175, 100, 49, 1280, 81, 196, 95, 240, 55, 500, 91, 576, 105, 124, 61, 560
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OFFSET
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1,2
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..10000
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FORMULA
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Multiplicative with a(p^e) = (p+2)^e.
If n = Product p(k)^e(k) then a(n) = Product (p(k)+2)^e(k).
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MATHEMATICA
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a166590[n_] := {1}~Join~Rest[Times @@ Power @@@ Transpose[{Plus[First /@ FactorInteger@ #, 2], Last /@ FactorInteger@ #}] & /@ Range@n]; a166590[60] (* Michael De Vlieger, Jan 07 2015 *)
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PROG
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(PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 1] += 2); factorback(f); \\ Michel Marcus, Jun 09 2014
(Python)
from math import prod
from sympy import factorint
def A166590(n): return prod((p+2)**e for p, e in factorint(n).items()) # Chai Wah Wu, Dec 26 2022
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CROSSREFS
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Sequence in context: A289742 A340850 A249113 * A244643 A085768 A166304
Adjacent sequences: A166587 A166588 A166589 * A166591 A166592 A166593
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KEYWORD
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nonn,mult
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AUTHOR
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Jaroslav Krizek, Oct 17 2009
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EXTENSIONS
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More terms from Michel Marcus, Jun 09 2014
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STATUS
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approved
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