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A353784
a(n) = sigma(n) / LCM_{p^e||n} sigma(p^e), where n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n.
7
1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 4, 3, 2, 1, 1, 1, 2, 3, 1, 4, 1, 1, 1, 3, 1, 1, 1, 1, 2, 7, 1, 1, 6, 1, 4, 3, 1, 2, 1, 1, 1, 1, 2, 12, 1, 1, 4, 6, 1, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 3, 1, 4, 6, 1, 2, 3, 1, 3, 2, 1, 4, 3, 2, 1, 1, 3, 1, 1, 1, 6, 1, 1, 8
OFFSET
1,10
FORMULA
a(n) = A000203(n) / A353783(n).
MATHEMATICA
Array[DivisorSigma[1, #]/(LCM @@ DivisorSigma[1, Power @@@ FactorInteger[#]]) &, 105] (* Michael De Vlieger, May 08 2022 *)
PROG
(PARI) A353784(n) = { my(f=factor(n)~); (sigma(n) / lcm(vector(#f, i, sigma(f[1, i]^f[2, i])))); };
CROSSREFS
Cf. A336547 (positions of 1's), A336548 (of terms > 1).
Cf. also A345045, A345047
Sequence in context: A051714 A023593 A353755 * A117544 A030393 A328391
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 08 2022
STATUS
approved