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A166590 Totally multiplicative sequence with a(p) = p+2 for prime p. 22
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = (p+2)^e.

If n = Product p(k)^e(k) then a(n) = Product (p(k)+2)^e(k).

MATHEMATICA

a166590[n_] := {1}~Join~Rest[Times @@ Power @@@ Transpose[{Plus[First /@ FactorInteger@ #, 2], Last /@ FactorInteger@ #}] & /@ Range@n]; a166590[60] (* Michael De Vlieger, Jan 07 2015 *)

PROG

(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

CROSSREFS

Sequence in context: A289742 A340850 A249113 * A244643 A085768 A166304

Adjacent sequences: A166587 A166588 A166589 * A166591 A166592 A166593

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Oct 17 2009

EXTENSIONS

More terms from Michel Marcus, Jun 09 2014

STATUS

approved

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Last modified January 29 01:41 EST 2023. Contains 359905 sequences. (Running on oeis4.)