A074107 a(n) = Product of (prime + 1) for first n primes - primorial (n); Sum of proper divisors of the n-th primorial.

0, 1, 6, 42, 366, 4602, 66738, 1231314, 25136790, 612982650, 18612572370, 602072009070, 23079296834790, 976751205195990, 43281303292150770, 2090585319354906990, 113506497027753468870, 6842978980142398176930, 426187457118982899608730, 29098035465450244144376910, 2102916875063497845451016610, 156173789584825539524342644530

Offset: 0

Author

Amarnath Murthy, Aug 22 2002

Keywords

• nonn

Examples

			a(3) = (2+1)*(3+1)*(5+1) - 2*3*5 = 72 - 30 = 42.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..349 (terms 1..349 from Harvey P. Dale)
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A001065, A002110, A003415, A024451, A051674, A054640, A070826, A348507.

Programs

Maple

for n from 1 to 25 do a[n] := product(ithprime(i)+1,i=1..n)-product(ithprime(i),i=1..n): od:seq(a[j],j=1..25);

Mathematica

Module[{nn=20,p,pr,pr1},p=Prime[Range[nn]];pr=FoldList[Times,1,p];pr1= FoldList[Times,1,p+1];#[[2]]-#[[1]]&/@Rest[Thread[{pr,pr1}]]](* Harvey P. Dale, Feb 07 2015 *)

PARI

A074107(n) = (prod(i=1,n,1+prime(i))-prod(i=1,n,prime(i))); \\ Antti Karttunen, Nov 19 2024

Formula

From Antti Karttunen, Nov 19 2024: (Start)

a(n) = A348507(A002110(n)) = A054640(n) - A002110(n) = A001065(A002110(n)).

a(n) >= A024451(n), because A348507(n) >= A003415(n).

For n >= 1, a(n) <= A070826(1+n) [= A002110(1+n)/2] < A051674(n).

(End)

Extensions

More terms from Sascha Kurz, Feb 01 2003

Term a(0)=0 prepended, data section further extended, and secondary definition added by Antti Karttunen, Nov 19 2024