A110957 - OEIS

%I #21 Jul 18 2024 04:35:07

%S 1,10,104,1128,13008,173376,2634624,42422400,722304000,13698201600,

%T 286505164800,6267431116800,143150760345600,3551498315366400,

%U 91568579493888000,2450311107084288000,67966128937598976000,1951860294503497728000,59922451994125271040000,1958517758582618849280000

%N a(n) = (Sum_{k=1..n} 1/c(k))*(Product_{j=1..n} c(j)), where c(j) is the j-th composite.

%e Since the first 3 composites are 4, 6 and 8, the third term of the sequence is (1/4 + 1/6 + 1/8) * 4 * 6 * 8 = 48 + 32 + 24 = 104.

%p c:=proc(n) if isprime(n)=false then n else fi end: C:=[seq(c(n),n=2..35)]: a:=n->sum(1/C[k],k=1..n)*product(C[j],j=1..n): seq(a(n),n=1..20); # _Emeric Deutsch_, Oct 06 2005

%t composite[n_] := FixedPoint[n + PrimePi[#] + 1&, n + PrimePi[n] + 1];

%t a[n_] := Sum[(1/composite[k]), {k, 1, n}]*Product[composite[j], {j, 1, n}];

%t Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, Jul 18 2024 *)

%Y Cf. A002808, A024451.

%K nonn

%O 1,2

%A _Leroy Quet_, Sep 26 2005

%E More terms from _Emeric Deutsch_, Oct 06 2005