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A183091 a(n) is the product of the divisors p^k of n where p is prime and k >= 1.

%I A183091 #37 Aug 31 2023 05:33:53
%S A183091 1,2,3,8,5,6,7,64,27,10,11,24,13,14,15,1024,17,54,19,40,21,22,23,192,
%T A183091 125,26,729,56,29,30,31,32768,33,34,35,216,37,38,39,320,41,42,43,88,
%U A183091 135,46,47,3072,343,250,51,104,53,1458
%N A183091 a(n) is the product of the divisors p^k of n where p is prime and k >= 1.
%C A183091 Product of n-th row of triangle A210208. - _Reinhard Zumkeller_, Mar 18 2012
%H A183091 Reinhard Zumkeller, <a href="/A183091/b183091.txt">Table of n, a(n) for n = 1..10000</a>
%F A183091 a(n) = A007955(n) / A183092(n).
%F A183091 Multiplicative with a(p^k) = p^(k*(k+1)/2).
%F A183091 The Dirichlet g.f. of a(n) / abs(A153038(n)) is Product_{k >= 0} zeta(s+k). - _Álvar Ibeas_, Nov 10 2014
%e A183091 For n = 12, set of such divisors is {1, 2, 3, 4}; a(12) = 1*2*3*4 = 24.
%p A183091 A183091 := proc(n) local a,d; a := 1 ;for d in numtheory[divisors](n) minus {1} do  if nops( numtheory[factorset](d)) = 1 then a := a*d; end if; end do: a ; end proc: # _R. J. Mathar_, Apr 14 2011
%t A183091 Table[Product[d, {d, Select[Divisors[n], Length[FactorInteger[#]] == 1 &]}], {n,1, 54}] (* _Geoffrey Critzer_, Mar 18 2015 *)
%t A183091 f[p_, e_] := p^(e*(e+1)/2); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Aug 31 2023 *)
%o A183091 (Haskell)
%o A183091 a183091 = product . a210208_row  -- _Reinhard Zumkeller_, Mar 18 2012
%o A183091 (PARI) a(n)=my(f=factor(n)); prod(i=1,#f~, f[i,1]^binomial(f[i,2]+1,2)) \\ _Charles R Greathouse IV_, Nov 11 2014
%Y A183091 Cf. A007955, A023888, A153038, A183092, A210208.
%K A183091 nonn,easy,mult
%O A183091 1,2
%A A183091 _Jaroslav Krizek_, Dec 25 2010