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 A253629 Multiplicative function defined for prime powers by a(p^e) = p^(e-1)(p+1) if p > 2 and a(2^e) = 2^(e-1). 2
 1, 1, 4, 2, 6, 4, 8, 4, 12, 6, 12, 8, 14, 8, 24, 8, 18, 12, 20, 12, 32, 12, 24, 16, 30, 14, 36, 16, 30, 24, 32, 16, 48, 18, 48, 24, 38, 20, 56, 24, 42, 32, 44, 24, 72, 24, 48, 32, 56, 30, 72, 28, 54, 36, 72, 32, 80, 30, 60, 48, 62, 32, 96, 32, 84, 48, 68, 36, 96, 48, 72, 48, 74, 38, 120, 40, 96, 56, 80, 48, 108, 42, 84, 64, 108, 44, 120, 48, 90, 72, 112, 48 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(1) is put to 1. a(n) = A001615(n) if n is odd and a(n) = A001615(n)/3 if n is even. This arithmetic function is a sort of modification of the Dedekind psi function (A001615). This modification is made in order to construct the additive arithmetic function A253630. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Colin Defant, An arithmetic function arising from the Dedekind psi function, arXiv:1501.00971 [math.NT], 2015. MAPLE seq(x * mul(`if`(p>2, p+1, 1)/p, p=numtheory:-factorset(x)), x = 1..100); # Robert Israel, Jan 08 2015 MATHEMATICA Table[If[EvenQ[n], (1/3) If[n > 1, n Times @@ (1 + 1/(Select[Divisors[n], PrimeQ])), 1], If[n > 1, n Times @@ (1 + 1/(Select[Divisors[n], PrimeQ])), 1]], {n, 260}] PROG (PARI) a(n)=my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]-1)*if(f[i, 1]>2, f[i, 1]+1, 1)) \\ Charles R Greathouse IV, Jan 08 2015 CROSSREFS Cf. A001615 (Dedekind psi function). Sequence in context: A161912 A162339 A200697 * A327095 A176836 A021705 Adjacent sequences:  A253626 A253627 A253628 * A253630 A253631 A253632 KEYWORD nonn,mult AUTHOR Colin Defant, Jan 06 2015 STATUS approved

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Last modified September 15 12:22 EDT 2019. Contains 327078 sequences. (Running on oeis4.)