OFFSET
0,3
REFERENCES
József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter IV, p. 144.
LINKS
Chai Wah Wu,Table of n, a(n) for n = 0..10000(terms n = 0..1000 from T. D. Noe)
Krishnaswami Alladi and Paul Erdős,On an additive arithmetic function,Pacific Journal of Mathematics, Vol. 71, No. 2 (1977), pp. 275-294;alternative link.
FORMULA
FromBenoit Cloitre,Apr 14 2002: (Start)
a(0)=0; for n>0, a(n) = Sum_{k=1..n}A001414(k).
Asymptotic formula: a(n) ~ (Pi^2/12)*n^2/log(n). [Proven by Alladi and Erdős (1977). -Amiram Eldar,Mar 04 2021]
(End)
MAPLE
a:= proc(n) option remember; `if`(n<2, 0,
a(n-1)+add(i[1]*i[2], i=ifactors(n)[2]))
end:
seq(a(n), n=0..60); #Alois P. Heinz,Apr 09 2021
MATHEMATICA
sopfr[n_]:= Plus @@ Times @@@ FactorInteger@ n; a[n_]:= a[n] = a[n - 1] + sopfr[n]; a[0] = a[1] = 0; Array[a, 59, 0] (*Robert G. Wilson v,May 18 2015 *)
PROG
(PARI) for(n=1, 100, print1(sum(k=1, n, sum(i=1, omega(k), component(component(factor(k), 1), i)*component(component(factor(k), 2), i))), "," ))
(Python)
from sympy import factorial, factorint
defA025281(n): return sum(p*e for p, e in factorint(factorial(n)).items()) #Chai Wah Wu,Apr 09 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved