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A331179 Number of values of k, 1 <= k <= n, with A173557(k) = A173557(n), where A173557(n) = Product_{p-1 | p is prime and divisor of n}.

%I A331179 #10 Jan 12 2022 04:09:28
%S A331179 1,2,1,3,1,2,1,4,3,2,1,4,1,2,1,5,1,5,1,3,2,2,1,6,4,3,7,3,1,2,1,6,1,2,
%T A331179 1,8,1,2,2,5,1,4,1,3,3,2,1,9,4,6,1,5,1,10,2,5,2,2,1,4,1,2,6,7,1,2,1,3,
%U A331179 1,3,1,11,1,3,5,3,2,4,1,7,12,3,1,7,1,2,1,4,1,6,2,3,3,2,3,13,1,6,3,8,1,2,1,8,2
%N A331179 Number of values of k, 1 <= k <= n, with A173557(k) = A173557(n), where A173557(n) = Product_{p-1 | p is prime and divisor of n}.
%C A331179 Ordinal transform of A173557.
%H A331179 Antti Karttunen, <a href="/A331179/b331179.txt">Table of n, a(n) for n = 1..65537</a>
%t A331179 A173557[n_] := If[n == 1, 1, Times @@ (FactorInteger[n][[All, 1]] - 1)];
%t A331179 Module[{b}, b[_] = 0;
%t A331179 a[n_] := With[{t = A173557[n]}, b[t] = b[t] + 1]];
%t A331179 Array[a, 105] (* _Jean-François Alcover_, Jan 12 2022 *)
%o A331179 (PARI)
%o A331179 up_to = 65537;
%o A331179 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 A331179 A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
%o A331179 v331179 = ordinal_transform(vector(up_to, n, A173557(n)));
%o A331179 A331179(n) = v331179[n];
%Y A331179 Cf. A173557.
%Y A331179 Cf. also A081373, A331175, A331178.
%K A331179 nonn
%O A331179 1,2
%A A331179 _Antti Karttunen_, Jan 11 2020