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

1, 3, 12, 7, 72, 28, 576, 15, 91, 168, 6912, 60, 96768, 1344, 546, 31, 1741824, 195, 34836480, 360, 4368, 16128, 836075520, 124, 2821, 225792, 600, 2880, 25082265600, 1170, 802632499200, 63, 52416, 4064256, 22568, 403, 30500034969600, 81285120, 733824, 744, 1281001468723200, 9360, 56364064623820800, 34560, 3600, 1950842880

Offset: 1

Author

Antti Karttunen, Aug 22 2020

Keywords

• nonn

Links

• Index entries for sequences related to primorial numbers
• Index entries for sequences related to sigma(n)

Crossrefs

Row 0 of A337205, and of A337472.

Cf. A000203, A034386, A108951, A337204.

Cf. also A323173.

Programs

Mathematica

Array[DivisorSigma[1, Apply[Times, FactorInteger[#] /. {p_, e_} /; e > 0 :> Apply[Times, Prime@ Range@ PrimePi@ p]^e]] &, 46] (* Michael De Vlieger, Aug 27 2020 *)

PARI

A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
A337203(n) = sigma(A108951(n));

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));

Formula

a(n) = A000203(A108951(n)).