A326043 Multiplicative with a(p^e) = floor[((e-1)+sigma(p^e)) / e].

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

Author

Antti Karttunen, Jun 04 2019

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000203, A048107, A325973.

Programs

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])));

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)).