A351260 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A046523(i) = A046523(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 47, 56, 2, 57, 58, 59, 2, 60, 41, 61, 62, 63, 2, 64, 37, 65, 66, 67, 68, 69, 2, 70, 71, 72, 2, 73, 2, 74, 56

Offset: 1

Author

Antti Karttunen, Feb 06 2022

Keywords

• nonn
• easy

Comments

Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A046523(n)].

For all i, j >= 1:

A305800(i) = A305800(j) => a(i) = a(j),

a(i) = a(j) => A294877(i) = A294877(j),

a(i) = a(j) => A300249(i) = A300249(j),

a(i) = a(j) => A344025(i) = A344025(j).

Links

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

Crossrefs

Cf. A003415, A003557, A046523.

Cf. also A305800, A294877, A300249, A344025.

Differs from A300235, A305895 and A327931 for the first time at n=105, where a(105) = 56, while A300235(105) = A305895(105) = A327931(105) = 75.

Differs from A300249 for the first time at n=425, where a(425) = 299, while A300249(425) = 198.

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
A003557(n) = (n/factorback(factorint(n)[, 1]));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux351260(n) = [A003415(n), A003557(n), A046523(n)];
v351260 = rgs_transform(vector(up_to,n,Aux351260(n)));
A351260(n) = v351260[n];