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A127482
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Product of the nonzero digital products of all the prime numbers prime(1) to prime(n).
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1
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2, 6, 30, 210, 210, 630, 4410, 39690, 238140, 4286520, 12859560, 270050760, 1080203040, 12962436480, 362948221440, 5444223321600, 244990049472000, 1469940296832000, 61737492466944000, 432162447268608000, 9075411392640768000, 571750917736368384000
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OFFSET
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1,1
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LINKS
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FORMULA
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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
a(n) = Product_{k=1..n} A051801(prime(k)).
a(n) = Product_{k=1..n} A101987(k). (End)
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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Rest[FoldList[Times, 1, Times@@Cases[IntegerDigits[#], Except[0]]&/@ Prime[ Range[ 20]]]] (* Harvey P. Dale, Mar 19 2013 *)
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PROG
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(PARI) f(n) = vecprod(select(x->(x>1), digits(prime(n)))); \\ A101987
(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)))
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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Alain Van Kerckhoven (alain(AT)avk.org), Sep 12 2007
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EXTENSIONS
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STATUS
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approved
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