A344572 - OEIS

%I #10 May 24 2021 00:44:39

%S 0,1,2,5,5,10,8,16,15,21,16,33,20,31,31,44,29,55,33,61,48,57,41,89,52,

%T 70,67,90,56,113,60,109,85,99,84,153,76,112,102,156,85,166,89,153,139,

%U 139,98,220,113,176,141,187,114,225,141,225,161,185,129,305,134,197,200,254

%N a(n) = Sum_{d|n} Omega(d!).

%H David A. Corneth, <a href="/A344572/b344572.txt">Table of n, a(n) for n = 1..10000</a>

%e a(10) = Sum_{d|10} Omega(d!) = Omega(1!) + Omega(2!) + Omega(5!) + Omega(10!) = 0 + 1 + 5 + 15 = 21.

%t Table[Sum[PrimeOmega[k!] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

%o (PARI) first(n) = { my(v = vector(n), res = vector(n), d); for(i = 2, n, v[i] = v[i-1] + bigomega(i); ); for(i = 2, n, d = divisors(i); res[i] = sum(i = 2, #d, v[d[i]]) ); res } \\ _David A. Corneth_, May 23 2021

%Y Cf. A000142, A001222 (Omega), A022559.

%K nonn

%O 1,3

%A _Wesley Ivan Hurt_, May 23 2021