A327970 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(n) = A003415(j) and A327936(i) = A327936(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, 19, 2, 20, 21, 22, 23, 24, 2, 12, 25, 26, 2, 27, 2, 28, 29, 30, 2, 31, 21, 32, 33, 34, 2, 35, 25, 36, 37, 19, 2, 36, 2, 38, 39, 40, 41, 42, 2, 43, 44, 45, 2, 46, 2, 29, 47, 20, 41, 48, 2, 49, 50, 51, 2, 52, 37, 32, 53, 54, 2, 55, 33, 56, 57, 58, 59, 60, 2, 61, 62, 54, 2, 63, 2, 64, 48

Offset: 1

Author

Antti Karttunen, Oct 01 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A003415(n), A327936(n)].

For all i, j:

a(i) = a(j) => A256750(i) = A256750(j),

a(i) = a(j) => A327932(i) = A327932(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003415, A256750, A327932, A327936.

Programs

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) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]>=f[k,1])); factorback(f); };
Aux327970(n) = [A003415(n), A327936(n)];
v327970 = rgs_transform(vector(up_to, n, Aux327970(n)));
A327970(n) = v327970[n];