A328113 Lexicographically earliest infinite sequence such that a(i) = a(j) => A327963(i) = A327963(j) for all i, j.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 3, 9, 10, 2, 11, 2, 12, 13, 14, 2, 15, 13, 5, 16, 17, 2, 18, 2, 11, 19, 20, 21, 22, 2, 11, 23, 24, 2, 25, 2, 26, 27, 8, 2, 28, 19, 29, 30, 31, 2, 32, 33, 34, 35, 18, 2, 36, 2, 37, 38, 39, 40, 41, 2, 42, 43, 44, 2, 45, 2, 27, 46, 47, 40, 48, 2, 49, 50, 51, 2, 52, 35, 29, 53, 54, 2, 55, 56, 57, 58, 36, 59, 60, 2, 61, 62, 63, 2, 64, 2, 65, 48

Offset

1,2

Comments

Restricted growth sequence transform of A327963(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]));
A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 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; };
A327963(n) = if(1==n, 0, my(u=A003415(n)); if(!A129251(u), u, A276086(n)));
v328113 = rgs_transform(vector(up_to, n, A327963(n)));
A328113(n) = v328113[n];

Crossrefs

Cf. A003415, A129251, A276086, A327928, A327929, A327963.

Sequence in context: A300240 A323168 A335425 * A326192 A323245 A323240

Adjacent sequences: A328110 A328111 A328112 * A328114 A328115 A328116

Keyword

nonn

Author

Antti Karttunen, Oct 07 2019

Status

approved