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

%I A127482 #23 Sep 20 2024 03:04:57
%S A127482 2,6,30,210,210,630,4410,39690,238140,4286520,12859560,270050760,
%T A127482 1080203040,12962436480,362948221440,5444223321600,244990049472000,
%U A127482 1469940296832000,61737492466944000,432162447268608000,9075411392640768000,571750917736368384000
%N A127482 Product of the nonzero digital products of all the prime numbers prime(1) to prime(n).
%H A127482 Harvey P. Dale, <a href="/A127482/b127482.txt">Table of n, a(n) for n = 1..547</a>
%F A127482 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
%F A127482 From _Michel Marcus_, Mar 11 2022: (Start)
%F A127482 a(n) = Product_{k=1..n} A051801(prime(k)).
%F A127482 a(n) = Product_{k=1..n} A101987(k). (End)
%e A127482 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.
%p A127482 a:= proc(n) option remember; `if`(n<1, 1, a(n-1)*mul(
%p A127482      `if`(i=0, 1, i), i=convert(ithprime(n), base, 10)))
%p A127482     end:
%p A127482 seq(a(n), n=1..30);  # _Alois P. Heinz_, Mar 11 2022
%t A127482 Rest[FoldList[Times,1,Times@@Cases[IntegerDigits[#],Except[0]]&/@ Prime[ Range[ 20]]]] (* _Harvey P. Dale_, Mar 19 2013 *)
%o A127482 (PARI) f(n) = vecprod(select(x->(x>1), digits(prime(n)))); \\ A101987
%o A127482 a(n) = prod(k=1, n, f(k)); \\ _Michel Marcus_, Mar 11 2022
%o A127482 (Python)
%o A127482 from math import prod
%o A127482 from sympy import sieve
%o A127482 def pod(s): return prod(int(d) for d in s if d != '0')
%o A127482 def a(n): return pod("".join(str(sieve[i+1]) for i in range(n)))
%o A127482 print([a(n) for n in range(1, 23)]) # _Michael S. Branicky_, Mar 11 2022
%Y A127482 Cf. A000040, A007953, A007954, A051801, A101987, A131385, A131387, A131451.
%K A127482 base,easy,nonn
%O A127482 1,1
%A A127482 Alain Van Kerckhoven (alain(AT)avk.org), Sep 12 2007
%E A127482 Corrected and extended by _Hieronymus Fischer_, Sep 29 2007