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
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..547
Programs
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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 *)
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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
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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
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)
Extensions
Corrected and extended by Hieronymus Fischer, Sep 29 2007