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

1,2

Links

Table of n, a(n) for n=1..46.

Index entries for sequences related to primorial numbers

Index entries for sequences related to sigma(n)

Formula

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

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 *)

Prog

(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));

Crossrefs

Row 0 of A337205, and of A337472.

Cf. A000203, A034386, A108951, A337204.

Cf. also A323173.

Sequence in context: A093855 A355338 A344112 * A013188 A234947 A051353

Adjacent sequences: A337200 A337201 A337202 * A337204 A337205 A337206

Keyword

nonn

Author

Antti Karttunen, Aug 22 2020

Status

approved