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Number of values of k, 1 <= k <= n, with f(k) = f(n), where f(n) = [A001222(n), A061395(n)].
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%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