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

%I A074107 #35 Nov 19 2024 17:24:06
%S A074107 0,1,6,42,366,4602,66738,1231314,25136790,612982650,18612572370,
%T A074107 602072009070,23079296834790,976751205195990,43281303292150770,
%U A074107 2090585319354906990,113506497027753468870,6842978980142398176930,426187457118982899608730,29098035465450244144376910,2102916875063497845451016610,156173789584825539524342644530
%N A074107 a(n) = Product of (prime + 1) for first n primes - primorial (n); Sum of proper divisors of the n-th primorial.
%H A074107 Antti Karttunen, <a href="/A074107/b074107.txt">Table of n, a(n) for n = 0..349</a> (terms 1..349 from Harvey P. Dale)
%H A074107 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A074107 From _Antti Karttunen_, Nov 19 2024: (Start)
%F A074107 a(n) = A348507(A002110(n)) = A054640(n) - A002110(n) = A001065(A002110(n)).
%F A074107 a(n) >= A024451(n), because A348507(n) >= A003415(n).
%F A074107 For n >= 1, a(n) <= A070826(1+n) [= A002110(1+n)/2] < A051674(n).
%F A074107 (End)
%e A074107 a(3) = (2+1)*(3+1)*(5+1) - 2*3*5 = 72 - 30 = 42.
%p A074107 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);
%t A074107 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 *)
%o A074107 (PARI) A074107(n) = (prod(i=1,n,1+prime(i))-prod(i=1,n,prime(i))); \\ _Antti Karttunen_, Nov 19 2024
%Y A074107 Cf. A001065, A002110, A003415, A024451, A051674, A054640, A070826, A348507.
%K A074107 nonn
%O A074107 0,3
%A A074107 _Amarnath Murthy_, Aug 22 2002
%E A074107 More terms from _Sascha Kurz_, Feb 01 2003
%E A074107 Term a(0)=0 prepended, data section further extended, and secondary definition added by _Antti Karttunen_, Nov 19 2024