A336147 Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A278221(i) = A278221(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Jul 12 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A020639(n), A278221(n)].

For all i, j:

A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j),

a(i) = a(j) => A243055(i) = A243055(j),

a(i) = a(j) => A336150(i) = A336150(j).

Links

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

Crossrefs

Cf. A020639, A046523, A122111, A278221.

Cf. also A243055, A286621, A318891, A324400, A336146, A336148, A336149, A336150.

First differs from A322590 at a(70) = 28 instead of 44.

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; };
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
Aux336147(n) = [A020639(n),A278221(n)];
v336147 = rgs_transform(vector(up_to, n, Aux336147(n)));
A336147(n) = v336147[n];