A110957 - OEIS

A110957

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

1, 10, 104, 1128, 13008, 173376, 2634624, 42422400, 722304000, 13698201600, 286505164800, 6267431116800, 143150760345600, 3551498315366400, 91568579493888000, 2450311107084288000, 67966128937598976000, 1951860294503497728000, 59922451994125271040000, 1958517758582618849280000

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

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.

MAPLE

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

MATHEMATICA

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

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

Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Jul 18 2024 *)

CROSSREFS

Cf. A002808, A024451.

Sequence in context: A190954 A163309 A163165 * A077671 A117833 A117832

Adjacent sequences: A110954 A110955 A110956 * A110958 A110959 A110960

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 26 2005

EXTENSIONS

More terms from Emeric Deutsch, Oct 06 2005

STATUS

approved