|
%I #11 Jan 10 2022 13:28:12
%S 1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,2,1,1,2,1,1,1,3,1,3,1,1,2,1,1,2,1,
%T 3,2,1,1,2,1,1,2,1,1,3,1,1,1,4,4,2,1,1,3,3,1,2,1,1,2,1,1,3,1,3,2,1,1,
%U 2,4,1,2,1,1,5,1,4,2,1,1,4,1,1,2,3,1,2,1,1,3,4,1,2,1,3,1,1,5,3,4,1,2,1,1,6
%N Number of values of k, 1 <= k <= n, with f(k) = f(n), where f(n) = [A001222(n), A061395(n)].
%C Ordinal transform of A331298, or equally, of the ordered pair [A001222(n), A061395(n)].
%H Antti Karttunen, <a href="/A331295/b331295.txt">Table of n, a(n) for n = 1..12000</a>
%H Antti Karttunen, <a href="/A331295/a331295.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%t f[n_] := f[n] = {PrimeOmega[n], PrimePi[FactorInteger[n]][[-1, 1]]};
%t a[n_] := Count[Array[f, n], f[n]];
%t Array[a, 105] (* _Jean-François Alcover_, Jan 10 2022 *)
%o (PARI)
%o up_to = 1001;
%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 A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
%o Aux331298(n) = [bigomega(n), A061395(n)];
%o v331295 = ordinal_transform(vector(up_to, n, Aux331298(n)));
%o A331295(n) = v331295[n];
%Y Cf. A001222, A061395, A078899, A331296, A331297, A331298.
%K nonn
%O 1,9
%A _Antti Karttunen_, Jan 19 2020
|
