|
|
A339308
|
|
Partial sums of products of proper divisors of n (A007956).
|
|
0
|
|
|
1, 2, 3, 5, 6, 12, 13, 21, 24, 34, 35, 179, 180, 194, 209, 273, 274, 598, 599, 999, 1020, 1042, 1043, 14867, 14872, 14898, 14925, 15709, 15710, 42710, 42711, 43735, 43768, 43802, 43837, 323773, 323774, 323812, 323851, 387851, 387852, 461940, 461941, 463877
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=1..n} pod(k)/k = Sum_{k=1..n} (A007955(k)/k) = Sum_{k=1..n} A007956(k).
|
|
EXAMPLE
|
a(6) = 12 = (1 + 1 + 1 + 2 + 1 + 6), where pod(n)/ n = 1, 1, 1, 2, 1, 6, 1, 8, 3, 10, 1, 144, ...
|
|
MATHEMATICA
|
popd[n_] := n^(DivisorSigma[0, n]/2 - 1); Accumulate @ Array[popd, 44] (* Amiram Eldar, Nov 30 2020 *)
|
|
PROG
|
(Magma) [&+[&*Divisors(k) / k: k in [1..n]]: n in [1..100]]
(PARI) a(n) = sum(k=1, n, vecprod(divisors(k))/k); \\ Michel Marcus, Nov 30 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|