A127482 - OEIS

%I #23 Sep 20 2024 03:04:57

%S 2,6,30,210,210,630,4410,39690,238140,4286520,12859560,270050760,

%T 1080203040,12962436480,362948221440,5444223321600,244990049472000,

%U 1469940296832000,61737492466944000,432162447268608000,9075411392640768000,571750917736368384000

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

%H Harvey P. Dale, <a href="/A127482/b127482.txt">Table of n, a(n) for n = 1..547</a>

%F 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 From _Michel Marcus_, Mar 11 2022: (Start)

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

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

%e 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 a:= proc(n) option remember; `if`(n<1, 1, a(n-1)*mul(

%p      `if`(i=0, 1, i), i=convert(ithprime(n), base, 10)))

%p     end:

%p seq(a(n), n=1..30);  # _Alois P. Heinz_, Mar 11 2022

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

%o (PARI) f(n) = vecprod(select(x->(x>1), digits(prime(n)))); \\ A101987

%o a(n) = prod(k=1, n, f(k)); \\ _Michel Marcus_, Mar 11 2022

%o (Python)

%o from math import prod

%o from sympy import sieve

%o def pod(s): return prod(int(d) for d in s if d != '0')

%o def a(n): return pod("".join(str(sieve[i+1]) for i in range(n)))

%o print([a(n) for n in range(1, 23)]) # _Michael S. Branicky_, Mar 11 2022

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

%K base,easy,nonn

%O 1,1

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

%E Corrected and extended by _Hieronymus Fischer_, Sep 29 2007