cp's OEIS Frontend

A337203 Sum of the divisors of the primorial inflation of n.

%I A337203 #11 Aug 28 2020 11:06:45
%S A337203 1,3,12,7,72,28,576,15,91,168,6912,60,96768,1344,546,31,1741824,195,
%T A337203 34836480,360,4368,16128,836075520,124,2821,225792,600,2880,
%U A337203 25082265600,1170,802632499200,63,52416,4064256,22568,403,30500034969600,81285120,733824,744,1281001468723200,9360,56364064623820800,34560,3600,1950842880
%N A337203 Sum of the divisors of the primorial inflation of n.
%H A337203 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%H A337203 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A337203 a(n) = A000203(A108951(n)).
%t A337203 Array[DivisorSigma[1, Apply[Times, FactorInteger[#] /. {p_, e_} /; e > 0 :> Apply[Times, Prime@ Range@ PrimePi@ p]^e]] &, 46] (* _Michael De Vlieger_, Aug 27 2020 *)
%o A337203 (PARI)
%o A337203 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A337203 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
%o A337203 A337203(n) = sigma(A108951(n));
%o A337203 (PARI) A337203(n) = if(1==n,n, my(f=factor(n), h = #f~, prevpid=primepi(f[h,1]), e=f[h,2], p, s=1); forstep(i=h-1,0,-1, if(!i,pid=0,pid=primepi(f[i,1])); forstep(j=prevpid,(1+pid),-1, p=prime(j); s *= ((p^(1+e)-1)/(p-1))); if(!pid,return(s)); prevpid = pid; e += f[i,2]); (s));
%Y A337203 Row 0 of A337205, and of A337472.
%Y A337203 Cf. A000203, A034386, A108951, A337204.
%Y A337203 Cf. also A323173.
%K A337203 nonn
%O A337203 1,2
%A A337203 _Antti Karttunen_, Aug 22 2020