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A353794
a(n) = A353791(sigma(A003961(n))), where A353791(n) = A003958(n) * A064989(n).
7
1, 1, 4, 132, 1, 4, 4, 12, 870, 1, 30, 528, 16, 4, 4, 4900, 12, 870, 4, 132, 16, 30, 48, 48, 1224, 16, 528, 528, 1, 4, 306, 3960, 120, 12, 4, 114840, 120, 4, 64, 12, 70, 16, 4, 3960, 870, 48, 64, 19600, 9180, 1224, 48, 2112, 48, 528, 30, 48, 16, 1, 870, 528, 208, 306, 3480, 1191372, 16, 120, 16, 1584, 192, 4, 1116
OFFSET
1,3
COMMENTS
It is conjectured that a(n) is not a multiple of A353793(n) on any other n except on n=1. See also A353795.
FORMULA
Multiplicative with a(p^e) = A003958(1 + q + ... + q^e) * A064989(1 + q + ... + q^e), where q is the least prime larger than p.
a(n) = A353791(A003973(n)) = A353792(A003961(n)).
a(n) = A326042(n) * A351456(n) = A064989(A003973(n)) * A003958(A003973(n)).
PROG
(PARI)
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353794(n) = { my(s=sigma(A003961(n))); (A003958(s)*A064989(s)); };
CROSSREFS
Cf. A000203, A003958, A003961, A003973, A064989, A326042, A351456, A353791, A353792, A353793, A353795 [numbers k such that k divides a(k)].
Cf. also A353790.
Sequence in context: A291172 A194536 A064227 * A204079 A252172 A192837
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 11 2022
STATUS
approved