A368695 - OEIS

A368695

Lexicographically earliest infinite sequence such that a(i) = a(j) => A368694(i) = A368694(j) for all i, j >= 0.

1, 2, 3, 4, 3, 5, 6, 7, 3, 8, 9, 10, 3, 11, 12, 13, 3, 14, 15, 13, 3, 16, 17, 18, 3, 19, 13, 20, 3, 21, 11, 4, 3, 22, 23, 24, 3, 21, 11, 25, 3, 26, 27, 28, 3, 29, 30, 5, 3, 31, 32, 33, 3, 8, 34, 21, 3, 35, 36, 11, 3, 20, 6, 7, 3, 37, 38, 39, 3, 40, 41, 42, 3, 35, 36, 43, 3, 44, 45, 8, 3, 46, 47, 48, 3, 49, 50, 35, 3

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OFFSET

0,2

COMMENTS

Restricted growth sequence transform of A368694, where A368694 is the Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

PROG

(PARI)

up_to = 65537;

rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };

A082903(n) = (2^valuation(sigma(n), 2));

memoA366889 = Map();

A366889(n) = if(1==n, 1, my(v); if(mapisdefined(memoA366889, n, &v), v, v = -sumdiv(n, d, if(d<n, A082903(n/d)*A366889(d), 0)); mapput(memoA366889, n, v); (v)));

A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

A368694(n) = A366889(A163511(n));

v368695 = rgs_transform(vector(1+up_to, n, A368694(n-1)));

A368695(n) = v368695[1+n];

CROSSREFS

Cf. A163511, A082903, A366889, A368694.

Sequence in context: A278056 A366880 A324345 * A324533 A377671 A141128

Adjacent sequences: A368692 A368693 A368694 * A368696 A368697 A368698

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Jan 03 2024

STATUS

approved