A328315 Lexicographically earliest infinite sequence such that a(i) = a(j) => A328099(i) = A328099(j) for all i, j.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 14, 17, 18, 11, 2, 7, 2, 12, 19, 20, 5, 21, 2, 12, 8, 22, 2, 23, 2, 24, 25, 26, 2, 27, 19, 28, 29, 30, 2, 31, 8, 32, 33, 34, 2, 35, 2, 36, 37, 38, 39, 40, 2, 41, 42, 43, 2, 44, 2, 25, 45, 46, 39, 47, 2, 48, 49, 50, 2, 51, 33, 28, 11, 52, 2, 53, 29, 54, 55, 35, 13, 56, 2, 57, 58, 52

Offset

1,2

Comments

Restricted growth sequence transform of A328099, defined as A328099(n) = min(A003415(n), A276086(n)).

Links

Antti Karttunen, Table of n, a(n) for n = 1..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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };
A328099(n) = min(A003415(n), A276086(n));
v328315 = rgs_transform(vector(up_to, n, A328099(n)));
A328315(n) = v328315[n];

Crossrefs

Cf. A003415, A276086, A328099, A328113.

Sequence in context: A319709 A293226 A373151 * A327970 A369448 A369047

Adjacent sequences: A328312 A328313 A328314 * A328316 A328317 A328318

Keyword

nonn

Author

Antti Karttunen, Oct 14 2019

Status

approved