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A354100
The 3-adic valuation of sigma, sum of divisors function.
4
0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 1, 3, 1, 0, 0, 1, 0, 2, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 0, 3, 1, 2, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 3, 1, 1, 2, 2, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 3, 0, 1, 1
OFFSET
1,10
FORMULA
a(n) = A007949(A000203(n)).
Additive with a(p^e) = A007949((p^(e+1)-1)/(p-1)).
MATHEMATICA
a[n_] := IntegerExponent[DivisorSigma[1, n], 3]; Array[a, 100] (* Amiram Eldar, May 18 2023 *)
PROG
(PARI) A354100(n) = valuation(sigma(n), 3);
(PARI) A354100(n) = { my(f=factor(n)); sum(k=1, #f~, valuation(((f[k, 1]^(f[k, 2]+1))-1)/(f[k, 1]-1), 3)); }; \\ Demonstrates the additivity
CROSSREFS
Cf. A329963 (positions of zeros), A087943 (of terms > 0).
Cf. also A336937, A354099.
Sequence in context: A321928 A321917 A115201 * A118229 A172250 A309047
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 17 2022
STATUS
approved