A127482 Product of the nonzero digital products of all the prime numbers prime(1) to prime(n).

2, 6, 30, 210, 210, 630, 4410, 39690, 238140, 4286520, 12859560, 270050760, 1080203040, 12962436480, 362948221440, 5444223321600, 244990049472000, 1469940296832000, 61737492466944000, 432162447268608000, 9075411392640768000, 571750917736368384000

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..547

Formula

a(n) = Product_{k=1..n} dp_p(prime(k) where prime(k)=A000040(k) and dp_p(m)=product of the nonzero digits of m in base p (p=10 for this sequence). - Hieronymus Fischer, Sep 29 2007

From Michel Marcus, Mar 11 2022: (Start)

a(n) = Product_{k=1..n} A051801(prime(k)).

a(n) = Product_{k=1..n} A101987(k). (End)

Example

a(7) = dp_10(2)*dp_10(3)*dp_10(5)*dp_10(7)*dp_10(11)*dp_10(13)*dp_10(17) = 2*3*5*7*(1*1)*(1*3)*(1*7) = 4410.

Maple

a:= proc(n) option remember; `if`(n<1, 1, a(n-1)*mul(
     `if`(i=0, 1, i), i=convert(ithprime(n), base, 10)))
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Mar 11 2022

Mathematica

Rest[FoldList[Times, 1, Times@@Cases[IntegerDigits[#], Except[0]]&/@ Prime[ Range[ 20]]]] (* Harvey P. Dale, Mar 19 2013 *)

Prog

(PARI) f(n) = vecprod(select(x->(x>1), digits(prime(n)))); \\ A101987
a(n) = prod(k=1, n, f(k)); \\ Michel Marcus, Mar 11 2022
(Python)
from math import prod
from sympy import sieve
def pod(s): return prod(int(d) for d in s if d != '0')
def a(n): return pod("".join(str(sieve[i+1]) for i in range(n)))
print([a(n) for n in range(1, 23)]) # Michael S. Branicky, Mar 11 2022

Crossrefs

Cf. A000040, A007953, A007954, A051801, A101987, A131385, A131387, A131451.

Sequence in context: A334317 A104561 A211211 * A372741 A118747 A129779

Adjacent sequences: A127479 A127480 A127481 * A127483 A127484 A127485

Keyword

base,easy,nonn

Author

Alain Van Kerckhoven (alain(AT)avk.org), Sep 12 2007

Extensions

Corrected and extended by Hieronymus Fischer, Sep 29 2007

Status

approved