A351236 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344025(i) = A344025(j) and A351085(i) = A351085(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, 21, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 41, 60, 61, 62, 2, 63, 64, 65

Offset: 1

Author

Antti Karttunen, Feb 06 2022

Keywords

• nonn
• easy
• look

Comments

Restricted growth sequence transform of the 4-tuple [A003415(n), A003557(n), A327858(n), A345000(n)].

Question: If an image-analysis algorithm were to classify the scatter plot of this sequence, where it would cluster it? Nearer to A344025 than to A351085?

Links

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

Crossrefs

Cf. A003415, A003557, A327858, A345000, A351085.

Differs from A344025 for the first time at n=91, where a(91) = 64, while A344025(91) = 37.

Cf. also A305800, A351235, A351260.

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) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327858(n) = gcd(A003415(n),A276086(n));
A345000(n) = gcd(A003415(n),A003415(A276086(n)));
Aux351236(n) = [A003415(n), A003557(n), A327858(n), A345000(n)];
v351236 = rgs_transform(vector(up_to, n, Aux351236(n)));
A351236(n) = v351236[n];