login
A337203
Sum of the divisors of the primorial inflation of n.
6
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
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. also A323173.
Sequence in context: A093855 A355338 A344112 * A013188 A234947 A051353
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 22 2020
STATUS
approved