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

0,3

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

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)

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A218817 A368321 A052589 * A187121 A225497 A336950

Adjacent sequences: A074104 A074105 A074106 * A074108 A074109 A074110

Keyword

nonn

Author

Amarnath Murthy, Aug 22 2002

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

Status

approved