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%I #17 Aug 02 2018 08:45:12
%S 1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,3,1,4,1,1,1,1,1,1,1,
%T 1,2,1,1,2,1,1,2,1,1,2,1,1,1,4,3,1,1,1,4,1,1,2,1,1,1,1,1,4,1,3,1,1,1,
%U 1,1,1,2,1,1,3,1,1,2,1,1,8,1,1,2,1,1,2,1,1,2,2,1,1,1,1,1,1,4,2,3,1,1,1,1,2,1,1,4,1,1,2,1,1,2,3,1,4,1,1,1
%N a(n) = A003963(n) / A290103(n).
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). Then a(n) is the product divided by the LCM of the integer partition with Heinz number n. - _Gus Wiseman_, Aug 01 2018
%H Antti Karttunen, <a href="/A290104/b290104.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A003963(n) / A290103(n).
%F Other identities. For all n >= 1:
%F a(A181819(n)) = A005361(n)/A072411(n).
%e n = 21 = 3 * 7 = prime(2) * prime(4), thus A003963(21) = 2*4 = 8, while A290103(21) = lcm(2,4) = 4, so a(21) = 8/4 = 2.
%t Table[If[n == 1, 1, Apply[Times, Map[PrimePi[#1]^#2 & @@ # &, #]] / Apply[LCM, PrimePi[#[[All, 1]] ]]] &@ FactorInteger@ n, {n, 120}] (* _Michael De Vlieger_, Aug 14 2017 *)
%o (Scheme) (define (A290104 n) (/ (A003963 n) (A290103 n)))
%Y Differs from A290106 for the first time at n=21.
%Y Cf. A003963, A056239, A074761, A289509, A290103, A290105, A296150, A316429, A316431.
%K nonn
%O 1,9
%A _Antti Karttunen_, Aug 13 2017
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