A117733 Sum of the n-th primorial and the n-th compositorial number.

2, 3, 7, 10, 34, 54, 234, 402, 1938, 17490, 19590, 209670, 237390, 2933070, 43575630, 696759630, 697240110, 12541643310, 12550832490, 250832355690

Offset

1,1

Comments

The primorial numbers A034386 define their exponential generating function

A034386(x) = sum_{n>=0} A034386(n)*x^n/n! = sum_{n>=0} x^n/A049614(n).

The compositorial numbers A049614 define their exponential generating function

A049614(x) = sum_{n>=0} A049614(n)*x^n/n! = sum_{n>=0} x^n/A034386(n).

Padding the values with A034386(n=0)=A049614(n=0)=1 at the beginning,

two special values of these are

A049614(x=1) = 4.5892461266379861713581024207350707369274... and

A034386(x=1) = 2.9200509773161347120925629171120194680027...

Links

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

Formula

a(n) = A034386(n)+A049614(n).

Mathematica

f[n_] := If[PrimeQ[n] == True, 1, n] cf[0] = 1; cf[n_Integer?Positive] := cf[n] = f[n]*cf[n - 1] g[n_] := If[PrimeQ[n] == True, n, 1] p[0] = 1; p[n_Integer?Positive] := p[n] = g[n]*p[n - 1] a=Table[cf[n] + p[n], {n, 1, 20}]

Crossrefs

Cf. A034386, A117683.

Sequence in context: A130968 A007748 A126617 * A066236 A118203 A263465

Adjacent sequences: A117730 A117731 A117732 * A117734 A117735 A117736

Keyword

nonn

Author

Roger L. Bagula, Apr 14 2006

Extensions

Offset and A-number corrected; comment rewritten - The Assoc Eds of the OEIS, Oct 20 2010

Status

approved