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%I #9 Dec 21 2021 12:04:01
%S 1,1,1,1,1,3,1,8,1,2,1,3,1,2,15,1,1,2,1,4,21,22,1,3,1,26,27,4,1,10,1,
%T 32,33,34,35,9,1,38,39,8,1,6,1,44,45,46,1,3,1,50,51,52,1,54,55,56,57,
%U 58,1,15,1,62,63,1,65,66,1,68,69,70,1,8,1,74,75,76,77,78,1,80,1,82,1,84,85,86,87,88,1,90
%N a(n) is n divided by the highest power of prime(A067004(n)) which divides it, where A067004 is the ordinal transform of number of divisors of n (A000005).
%H Antti Karttunen, <a href="/A331187/b331187.txt">Table of n, a(n) for n = 1..10000</a>
%H Antti Karttunen, <a href="/A331187/a331187.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(n) = n / (A000040(A067004(n))^A331186(n)).
%t b[_] = 0;
%t A067004[n_] := A067004[n] = With[{t = DivisorSigma[0, n]}, b[t] = b[t]+1];
%t A331186[n_] := IntegerExponent[n, Prime[A067004[n]]];
%t a[n_] := n/(Prime[A067004[n]]^A331186[n]);
%t Array[a, 105] (* _Jean-François Alcover_, Dec 21 2021 *)
%o (PARI)
%o up_to = 65537;
%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o v067004 = ordinal_transform(vector(up_to,n,numdiv(n)));
%o A067004(n) = v067004[n];
%o A331187(n) = { my(p=prime(A067004(n))); n/(p^valuation(n,p)); };
%Y Cf. A000040, A067004, A331186.
%Y Cf. also A331185.
%K nonn
%O 1,6
%A _Antti Karttunen_, Jan 12 2020
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