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A353792
a(n) = A003958(sigma(n)) * A064989(sigma(n)).
5
1, 4, 1, 30, 4, 4, 1, 48, 132, 16, 4, 30, 30, 4, 4, 870, 16, 528, 12, 120, 1, 16, 4, 48, 870, 120, 12, 30, 48, 16, 1, 480, 4, 64, 4, 3960, 306, 48, 30, 192, 120, 4, 70, 120, 528, 16, 4, 870, 1224, 3480, 16, 900, 64, 48, 16, 48, 12, 192, 48, 120, 870, 4, 132, 14238, 120, 16, 208, 480, 4, 16, 16, 6336, 1116, 1224, 870
OFFSET
1,2
FORMULA
Multiplicative with a(p^e) = A003958(1 + p + ... + p^e) * A064989(1 + p + ... + p^e).
a(n) = A353791(A000203(n)).
a(n) = A351442(n) * A350073(n) = A003958(A000203(n)) * A064989(A000203(n)).
PROG
(PARI)
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353792(n) = { my(s=sigma(n)); (A003958(s)*A064989(s)); };
(PARI) A353792(n) = { my(f=factor(n), s); prod(i=1, #f~, s = sigma(f[i, 1]^f[i, 2]); A003958(s)*A064989(s)); };
CROSSREFS
Cf. A046528 (positions of 1's).
Cf. also A353750.
Sequence in context: A350759 A077097 A190647 * A123126 A303277 A174501
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 11 2022
STATUS
approved