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

Author

Roger L. Bagula, Apr 14 2006

Keywords

• nonn

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...

Crossrefs

Cf. A034386, A117683.

Programs

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}]

Formula

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

Extensions

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