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A350073
a(n) = A064989(sigma(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.
10
1, 2, 1, 5, 2, 2, 1, 6, 11, 4, 2, 5, 5, 2, 2, 29, 4, 22, 3, 10, 1, 4, 2, 6, 29, 10, 3, 5, 6, 4, 1, 20, 2, 8, 2, 55, 17, 6, 5, 12, 10, 2, 7, 10, 22, 4, 2, 29, 34, 58, 4, 25, 8, 6, 4, 6, 3, 12, 6, 10, 29, 2, 11, 113, 10, 4, 13, 20, 2, 4, 4, 66, 31, 34, 29, 15, 2, 10, 3, 58, 49, 20, 10, 5, 8, 14, 6, 12, 12, 44, 5, 10
OFFSET
1,2
FORMULA
Multiplicative with a(p^e) = A064989(1 + p + p^2 + ... + p^e).
a(n) = A064989(A000203(n)) = A064989(A161942(n)).
MATHEMATICA
f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[DivisorSigma[1, n]]; Array[a, 100] (* Amiram Eldar, Dec 12 2021 *)
PROG
(PARI)
A064989(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = if(2==f[i, 1], 1, precprime(f[i, 1]-1))); factorback(f); };
A350073(n) = A064989(sigma(n));
CROSSREFS
Cf. also A326042, A350072.
Sequence in context: A371305 A308698 A308569 * A174978 A110874 A010253
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Dec 12 2021
STATUS
approved