The On-Line Encyclopedia of Integer Sequences (OEIS)

A344459 revision #4

A344459

a(n) = Sum_{d|n} d^Omega(d).

1, 3, 4, 19, 6, 42, 8, 531, 85, 108, 12, 1786, 14, 206, 234, 66067, 18, 5955, 20, 8124, 452, 498, 24, 334074, 631, 692, 19768, 22174, 30, 27372, 32, 33620499, 1104, 1176, 1238, 1687315, 38, 1466, 1538, 2568636, 42, 74774, 44, 85698, 91440, 2142, 48, 255203578, 2409

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OFFSET

1,2

COMMENTS

If p is prime, a(n) = Sum_{d|p} d^Omega(d) = 1^0 + p^1 = p + 1.

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

a(8) = Sum_{d|8} d^Omega(d) = 1^0 + 2^1 + 4^2 + 8^3 = 531.

MATHEMATICA

Table[Sum[k^PrimeOmega[k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]

CROSSREFS