A330755 - OEIS

%I #10 Jan 10 2022 12:49:16

%S 1,1,1,1,1,2,1,1,1,3,1,2,1,4,3,1,1,5,1,2,4,6,1,5,1,7,1,3,1,8,1,1,6,9,

%T 2,4,1,10,7,3,1,11,1,5,4,12,1,8,1,13,9,6,1,14,5,2,10,15,1,11,1,16,3,1,

%U 6,17,1,7,12,18,1,2,1,19,13,8,4,20,1,7,1,21,1,14,8,22,15,3,1,23,5,9,16,24,9,17,1,25,2,10,1,26,1,4,18

%N Number of values of k, 1 <= k <= n, with A034684(k) = A034684(n), where A034684 gives the smallest unitary divisor of n that is larger than 1.

%C Ordinal transform of A034684.

%H Antti Karttunen, <a href="/A330755/b330755.txt">Table of n, a(n) for n = 1..65537</a>

%t A034684[n_] := With[{f = FactorInteger[n]}, Min[f[[All, 1]]^f[[All, 2]]]];

%t Module[{b}, b[_] = 0;

%t a[n_] := With[{t = A034684[n]}, b[t] = b[t] + 1]];

%t Array[a, 105] (* _Jean-François Alcover_, Jan 10 2022 *)

%o (PARI)

%o up_to = 65537;

%o A034684(n) = if(1==n,n,my(f=factor(n)); vecmin(vector(#f[, 1], i, f[i, 1]^f[i, 2]))); \\ After code in A034699

%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 v330755 = ordinal_transform(vector(up_to, n, A034684(n)));

%o A330755(n) = v330755[n];

%Y Cf. A034684, A078898, A303759.

%K nonn

%O 1,6

%A _Antti Karttunen_, Dec 30 2019