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A215454 a(n) = least positive k such that n^2 divides k!

%I A215454 #15 Aug 01 2025 19:01:22
%S A215454 1,4,6,6,10,6,14,8,9,10,22,6,26,14,10,10,34,9,38,10,14,22,46,8,20,26,
%T A215454 15,14,58,10,62,12,22,34,14,9,74,38,26,10,82,14,86,22,10,46,94,10,28,
%U A215454 20,34,26,106,15,22,14,38,58,118,10,122,62,14,16,26,22,134,34
%N A215454 a(n) = least positive k such that n^2 divides k!
%C A215454 Indices n such that a(n)=n: 1 followed by A074845.
%e A215454 a(12): least positive k such that 144 divides k! is k=6, 6!=720. So a(12)=6.
%t A215454 Module[{nn=200,f},f=Range[nn]!;Position[f,#]&/@Table[SelectFirst[ f, Divisible[ #,n^2]&],{n,nn}]]//Flatten (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Dec 11 2018 *)
%o A215454 (Python)
%o A215454 TOP = 77
%o A215454 ii = [0]*TOP
%o A215454 for i in range(1, TOP):
%o A215454     ii[i] = i*i
%o A215454 f = k = y = 1
%o A215454 res = [-1]*TOP
%o A215454 while y<TOP:
%o A215454     for i in range(1, TOP):
%o A215454       if res[i]<0 and f % ii[i] == 0:
%o A215454         res[i] = k
%o A215454         y += 1
%o A215454     k += 1
%o A215454     f *= k
%o A215454 for i in range(1, TOP):
%o A215454     print(res[i], end=', ')
%Y A215454 Cf. A002034 (least k such that n divides k!).
%Y A215454 Cf. A085779 (least k such that triangular(n) divides k!).
%Y A215454 Cf. A093896 (least positive k such that n^n divides k!).
%K A215454 nonn
%O A215454 1,2
%A A215454 _Alex Ratushnyak_, Aug 11 2012