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A326043
Multiplicative with a(p^e) = floor[((e-1)+sigma(p^e)) / e].
4
1, 3, 4, 4, 6, 12, 8, 5, 7, 18, 12, 16, 14, 24, 24, 8, 18, 21, 20, 24, 32, 36, 24, 20, 16, 42, 14, 32, 30, 72, 32, 13, 48, 54, 48, 28, 38, 60, 56, 30, 42, 96, 44, 48, 42, 72, 48, 32, 29, 48, 72, 56, 54, 42, 72, 40, 80, 90, 60, 96, 62, 96, 56, 22, 84, 144, 68, 72, 96, 144, 72, 35, 74, 114, 64, 80, 96, 168, 80, 48, 31, 126
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = floor[(1/e) * (-1 + e + (((p^(1+e)) - 1)/(p-1)))].
a(n) <= A000203(n).
a(A048107(n)) = A325973(A048107(n)).
PROG
(PARI) A326043(n) = if(1==n, n, my(f = factor(n)); prod(i=1, #f~, floor((1/f[i, 2]) * ((f[i, 2]-1) + (((f[i, 1]^(1+f[i, 2])) - 1)/(f[i, 1]-1))))));
(PARI) A326043(n) = if(1==n, n, my(f = factor(n)); prod(i=1, #f~, floor( ((f[i, 2]-1)+sigma(f[i, 1]^f[i, 2])) / f[i, 2])));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Jun 04 2019
STATUS
approved