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A353278 Ordinal transform of the function f(n) = [A020639(n), A341353(n)] for n > 1, with f(1) = 1.

%I A353278 #9 Apr 11 2022 20:48:40
%S A353278 1,1,1,1,1,2,1,3,1,1,1,4,1,5,2,2,1,6,1,7,1,3,1,8,1,9,3,10,1,4,1,11,4,
%T A353278 5,2,1,1,12,2,6,1,13,1,14,5,2,1,15,1,16,6,17,1,18,1,19,3,20,1,21,1,7,
%U A353278 7,2,3,8,1,22,8,23,1,24,1,25,9,26,2,27,1,28,4,9,1,10,2,29,1,3,1,3,1,30,10,4,4,31,1
%N A353278 Ordinal transform of the function f(n) = [A020639(n), A341353(n)] for n > 1, with f(1) = 1.
%C A353278 Also the ordinal transform of A353277.
%H A353278 Antti Karttunen, <a href="/A353278/b353278.txt">Table of n, a(n) for n = 1..65537</a>
%H A353278 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A353278 (PARI)
%o A353278 up_to = 65537;
%o A353278 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 A353278 A007814(n) = valuation(n,2);
%o A353278 A007949(n) = valuation(n,3);
%o A353278 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A353278 Aux353278(n) = if(1==n,1,my(u=A156552(n)); [A007814(u), A007949(u)]);
%o A353278 v353278 = ordinal_transform(vector(up_to, n, Aux353278(n)));
%o A353278 A353278(n) = v353278[n];
%Y A353278 Cf. A007814, A007949, A020639, A156552, A341353, A353277.
%Y A353278 Cf. also A078898, A126760.
%K A353278 nonn
%O A353278 1,6
%A A353278 _Antti Karttunen_, Apr 10 2022