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A117733 Sum of the n-th primorial and the n-th compositorial number. 1

%I

%S 2,3,7,10,34,54,234,402,1938,17490,19590,209670,237390,2933070,

%T 43575630,696759630,697240110,12541643310,12550832490,250832355690

%N Sum of the n-th primorial and the n-th compositorial number.

%C The primorial numbers A034386 define their exponential generating function

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

%C The compositorial numbers A049614 define their exponential generating function

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

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

%C two special values of these are

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

%C A034386(x=1) = 2.9200509773161347120925629171120194680027...

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

%t 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}]

%Y Cf. A034386, A117683.

%K nonn

%O 1,1

%A _Roger L. Bagula_, Apr 14 2006

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

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Last modified March 7 13:24 EST 2021. Contains 341886 sequences. (Running on oeis4.)