A286630 a(0) = 1; for n >= 1, a(n) = A000040(n) * A002110(n).

1, 4, 18, 150, 1470, 25410, 390390, 8678670, 184294110, 5131136010, 187621103670, 6217375194030, 274567310987970, 12474260804615610, 562558737261811290, 28899819781659096270, 1727225399291072370690, 113442860659098545705130, 7154591262923825229979470, 526507543922377892743899030, 39613798938995626228686492690

Offset: 0

Author

Antti Karttunen, Jul 07 2017

Keywords

• nonn

Comments

The terms a(0) .. a(5), when viewed in primorial base (A049345) look as: 1, 20, 300, 5000, 70000, E00000, where "E" stands for the digit eleven.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..120
• Index entries for sequences related to primorial base

Crossrefs

Cf. A000040, A001248, A002110, A286629.

Subsequence of A276155.

Programs

Mathematica

Table[If[n==0, 1, Prime[n] Product[Prime[k], {k, n}]], {n, 0, 100}] (* Indranil Ghosh, Jul 07 2017 *)

PARI

a(n) = if (n==0, 1, prime(n)*prod(k=1, n, prime(k))); \\ Michel Marcus, Jul 07 2017

Python

from sympy import prime, primorial
def a002110(n): return 1 if n<1 else primorial(n)
def a(n): return 1 if n==0 else prime(n)*a002110(n)
print([a(n) for n in range(41)]) # Indranil Ghosh, Jul 07 2017

Scheme

(define (A286630 n) (if (zero? n) 1 (* (A000040 n) (A002110 n))))

Formula

a(0) = 1; for n >= 1, a(n) = A000040(n) * A002110(n).

For n >= 1, a(n) = A001248(n) * A002110(n-1) = A002110(n) + A286629(n).