The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A344459 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A344459

a(n) = Sum_{d|n} d^Omega(d).
(history; published version)

#4 by Wesley Ivan Hurt at Wed May 19 23:49:52 EDT 2021

STATUS

proposed

approved

#3 by Wesley Ivan Hurt at Wed May 19 21:51:09 EDT 2021

STATUS

editing

proposed

#2 by Wesley Ivan Hurt at Wed May 19 21:50:49 EDT 2021

NAME

allocated for Wesley Ivan Hurt

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

DATA

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

OFFSET

1,2

COMMENTS

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

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

Cf. A001222 (Omega).

KEYWORD

allocated

nonn

AUTHOR

Wesley Ivan Hurt, May 19 2021

STATUS

approved

editing

#1 by Wesley Ivan Hurt at Wed May 19 21:50:49 EDT 2021

NAME

allocated for Wesley Ivan Hurt

KEYWORD

allocated

STATUS

approved