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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.)