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%I #26 Aug 11 2024 17:18:37
%S 1,2,1,2,1,3,1,2,1,2,1,4,1,2,1,2,1,3,1,2,1,2,1,4,1,2,1,2,1,3,1,2,1,2,
%T 1,4,1,2,1,2,1,3,1,2,1,2,1,4,1,2,1,2,1,3,1,2,1,2,1,6,1,2,1,2,1,3,1,2,
%U 1,2,1,4,1,2,1,2,1,3,1,2,1,2,1,4,1,2,1
%N a(n) is the largest m such that m! divides n^2; a(n) = A055881(n^2).
%C For all n, A055881(n) <= a(n), and probably also a(n) <= A055874(n).
%C Moreover, a(n) > A055881(n) if and only if A055874(n) > A055881(n), thus A055926 gives (also) all the positions where this sequence differs from A055881. Please see Comments section in A055926 for the proof.
%C Differs from A055874 for the first time at n=840, where a(840)=7, while A055874(840)=8. A232099 gives all the positions where such differences occur.
%H Antti Karttunen, <a href="/A232098/b232098.txt">Table of n, a(n) for n = 1..10080</a>
%F a(n) = A055881(A000290(n)) = A055881(n^2).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A065887(k) = 1.78672776922161809767... . - _Amiram Eldar_, Jan 01 2024
%t Module[{nn=10,fct},fct=Table[{f,f!},{f,nn}];Table[Select[fct,Mod[n^2,#[[2]]]==0&][[-1,1]],{n,90}]] (* _Harvey P. Dale_, Aug 11 2024 *)
%o (Scheme)
%o (define (A232098 n) (A055881 (A000290 n)))
%Y Cf. A055881, A055874, A055926, A065887, A232096, A232099, A233267.
%K nonn,changed
%O 1,2
%A _Antti Karttunen_, Nov 18 2013
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