OFFSET
0,4
COMMENTS
Also sum of exponents in prime-power factorization of hyperfactorial(n) / superfactorial(n).
LINKS
Jeffrey C. Lagarias, Harsh Mehta, Products of binomial coefficients and unreduced Farey fractions, arXiv:1409.4145 [math.NT], 2014.
Eric Weisstein's World of Mathematics, Hyperfactorial
Eric Weisstein's World of Mathematics, Superfactorial
EXAMPLE
a(4) = 6 because C(4,0)*C(4,1)*C(4,2)*C(4,3)*C(4,4) = 2^5 * 3^1 and 5 + 1 = 6, where C(n,k) is the binomial coefficient.
MATHEMATICA
Array[Sum[PrimeOmega@ Binomial[#, k], {k, 0, #}] &, 57] (* Michael De Vlieger, Jan 19 2019 *)
PROG
(PARI) a(n) = sum(k=0, n, bigomega(binomial(n, k)));
(PARI) a(n) = my(t=0); sum(k=1, n, my(b=bigomega(k)); t+=b; k*b-t);
(PARI) first(n) = my(res = List([0]), r=0, t=0, b=0); for(k=1, n, b=bigomega(k); t += b; r += k*b-t; listput(res, r)); res \\ adapted from Daniel Suteu \\ David A. Corneth, Jan 16 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Suteu, Jan 15 2019
STATUS
approved