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A166640 Totally multiplicative sequence with a(p) = 9*(p-1) for prime p. 1
1, 9, 18, 81, 36, 162, 54, 729, 324, 324, 90, 1458, 108, 486, 648, 6561, 144, 2916, 162, 2916, 972, 810, 198, 13122, 1296, 972, 5832, 4374, 252, 5832, 270, 59049, 1620, 1296, 1944, 26244, 324, 1458, 1944, 26244, 360, 8748, 378, 7290, 11664, 1782, 414, 118098 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (9*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)-1)^e(k).
a(n) = A165830(n) * A003958(n) = 9^bigomega(n) * A003958(n) = 9^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]*9^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (9*(p-1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)
PROG
(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 9*(f[k, 1]-1)); factorback(f); } \\ Michel Marcus, May 21 2016
CROSSREFS
Sequence in context: A295473 A255839 A361082 * A140149 A197345 A186951
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Oct 18 2009
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)