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A166633 Totally multiplicative sequence with a(p) = 3*(p-1) for prime p. 3
1, 3, 6, 9, 12, 18, 18, 27, 36, 36, 30, 54, 36, 54, 72, 81, 48, 108, 54, 108, 108, 90, 66, 162, 144, 108, 216, 162, 84, 216, 90, 243, 180, 144, 216, 324, 108, 162, 216, 324, 120, 324, 126, 270, 432, 198, 138, 486, 324, 432 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = (3*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)-1)^e(k). a(n) = A165824(n) * A003958(n) = 3^bigomega(n) * A003958(n) = 3^A001222(n) * A003958(n).

MATHEMATICA

DirichletInverse[f_][1] = 1/f[1]; DirichletInverse[f_][n_] :=

DirichletInverse[f][n] = -1/f[1]*Sum[f[n/d]*DirichletInverse[f][d], {d, Most[Divisors[n]]}]; muphi[n_] := MoebiusMu[n]*EulerPhi[n]; a[m_] := DirichletInverse[muphi][m]; Table[a[m]*3^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)

PROG

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 3*(f[k, 1]-1)); factorback(f); } \\ Michel Marcus, May 20 2016

CROSSREFS

Cf. A001222, A003958, A165824, A166634.

Sequence in context: A213685 A271449 A261956 * A310154 A253277 A310155

Adjacent sequences:  A166630 A166631 A166632 * A166634 A166635 A166636

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Oct 18 2009

STATUS

approved

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Last modified November 14 19:12 EST 2018. Contains 317214 sequences. (Running on oeis4.)