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%I #24 Oct 26 2019 22:26:39
%S 1,2,3,1,5,6,7,0,3,10,11,3,13,14,15,0,17,6,19,5,21,22,23,0,10,26,1,7,
%T 29,30,31,0,33,34,35,3,37,38,39,0,41,42,43,11,15,46,47,0,21,20,51,13,
%U 53,2,55,0,57,58,59,15,61,62,21,0,65,66
%N If n = Product (p_j^e_j) then a(n) = Product (binomial(p_j, e_j)).
%H Reinhard Zumkeller, <a href="/A182938/b182938.txt">Table of n, a(n) for n = 1..10000</a>
%F a(A185359(n)) = 0. - _Reinhard Zumkeller_, Feb 18 2012
%F Dirichlet g.f.: Product_{p prime} (1 + p^(-s))^p. - _Ilya Gutkovskiy_, Oct 26 2019
%p A182938 := proc(n) local e,j; e := ifactors(n)[2]:
%p mul (binomial(e[j][1], e[j][2]), j=1..nops(e)) end:
%p seq (A182938(n), n=1..100);
%t a[n_] := Times @@ (Map[Binomial @@ # &, FactorInteger[n], 1]);
%t Table[a[n], {n, 1, 100}] (-Kellen Myers)
%o (PARI) a(n)=prod(i=1,#n=factor(n)~,binomial(n[1,i],n[2,i])) \\ - M. F. Hasler
%o (Haskell)
%o a182938 n = product $ zipWith a007318'
%o (a027748_row n) (map toInteger $ a124010_row n)
%o -- _Reinhard Zumkeller_, Feb 18 2012
%Y Cf. A000026, A001414, A008473, A008474, A008475, A008476, A008477, A028310, A069799.
%Y Cf. A027748, A124010, A007318.
%K nonn,mult
%O 1,2
%A _Peter Luschny_, Jan 16 2011
%E Given terms checked with new PARI code by _M. F. Hasler_, Jan 16 2011
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