|
|
A303279
|
|
Expansion of (1/(1 - x)^2) * Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)).
|
|
9
|
|
|
0, 1, 3, 7, 12, 19, 27, 38, 51, 66, 82, 101, 121, 143, 167, 195, 224, 256, 289, 325, 363, 403, 444, 489, 536, 585, 637, 692, 748, 807, 867, 932, 999, 1068, 1139, 1214, 1290, 1368, 1448, 1532, 1617, 1705, 1794, 1886, 1981, 2078, 2176, 2279, 2384, 2492, 2602, 2715, 2829, 2947, 3067
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Sum of exponents in prime-power factorization of product of first n factorials (A000178).
|
|
LINKS
|
|
|
EXAMPLE
|
a(5) = 12 because 2!*3!*4!*5! = 2^8*3^3*5 and 8 + 3 + 1 = 12.
|
|
MAPLE
|
b:= proc(n) option remember; `if`(n<1, [0$2],
(p-> p+[numtheory[bigomega](n), p[1]])(b(n-1)))
end:
a:= n-> b(n+1)[2]:
|
|
MATHEMATICA
|
nmax = 55; Rest[CoefficientList[Series[1/(1 - x)^2 Sum[Boole[PrimePowerQ[k]] x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
Table[PrimeOmega[BarnesG[n + 2]], {n, 55}]
Table[ Sum[ PrimeOmega@ j, {k, n}, {j, k}], {n, 55}]
|
|
PROG
|
(PARI) a(n) = my(t=0); sum(k=1, n, t+=bigomega(k)); \\ Daniel Suteu, Jan 17 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|