A380497 Euler transform of primorial numbers.

1, 2, 9, 46, 314, 3072, 37641, 603510, 11148030, 249327430, 7040987792, 216220333314, 7895699690498, 321315600822232, 13770543972819903, 644232544408157820, 33954066516677635554, 1994206929690480710244, 121461036181617491970561, 8111955386813996410196454, 574814471423312085719652432

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Eric Weisstein's World of Mathematics, Primorial.

Formula

G.f.: Product_{k>=1} 1 / (1 - x^k)^prime(k)#.

Maple

p:= proc(n) option remember; `if`(n<1, 1, p(n-1)*ithprime(n)) end:
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*
      add(d*p(d), d=numtheory[divisors](j)), j=1..n)/n)
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Jan 25 2025

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1 - x^k)^Product[Prime[j], {j, k}], {k, 1, nmax}], {x, 0, nmax}], x]
primorial[n_] := Product[Prime[j], {j, 1, n}]; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d primorial[d], {d, Divisors[j]}] a[n - j], {j, 1, n}]/n]; Table[a[n], {n, 0, 20}]

Crossrefs

Cf. A002110, A030009, A030012, A107895, A380498.

Sequence in context: A365855 A373312 A134091 * A219614 A183166 A032331

Adjacent sequences: A380494 A380495 A380496 * A380498 A380499 A380500

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 25 2025

Status

approved