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A354099
The 3-adic valuation of Euler totient function phi.
4
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 1, 1, 1, 0, 3, 0, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 1, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1
OFFSET
1,19
LINKS
FORMULA
a(n) = A007949(A000010(n)).
Additive with a(p^e) = A007949((p-1)*p^(e-1)).
MATHEMATICA
a[n_] := IntegerExponent[EulerPhi[n], 3]; Array[a, 100] (* Amiram Eldar, May 17 2022 *)
PROG
(PARI) A354099(n) = valuation(eulerphi(n), 3);
(PARI) A354099(n) = { my(f=factor(n)); sum(k=1, #f~, valuation((f[k, 1]-1)*(f[k, 1]^(f[k, 2]-1)), 3)); }; \\ Demonstrates the additivity.
CROSSREFS
Cf. A088232 (positions of zeros), A066498 (of terms > 0).
Cf. also A354100.
Sequence in context: A123758 A231642 A288318 * A219483 A239927 A069846
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 17 2022
STATUS
approved