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

Author

Antti Karttunen, Apr 10 2022

Keywords

• nonn

Comments

Also the ordinal transform of A353277.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A007814, A007949, A020639, A156552, A341353, A353277.

Cf. also A078898, A126760.

Programs

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];