A353278 Ordinal transform of the function f(n) = [A020639(n), A341353(n)] for n > 1, with f(1) = 1.
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, 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, 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
Offset: 1
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PARI
up_to = 65537; 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; }; A007814(n) = valuation(n,2); A007949(n) = valuation(n,3); 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 }; Aux353278(n) = if(1==n,1,my(u=A156552(n)); [A007814(u), A007949(u)]); v353278 = ordinal_transform(vector(up_to, n, Aux353278(n))); A353278(n) = v353278[n];
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