A372570 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A009194(n), A009195(n), A009223(n), A322361(n), A342671(n)], for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, May 25 2024

Keywords

• nonn

Comments

Restricted growth sequence transform of the quintuple [A009194(n), A009195(n), A009223(n), A322361(n), A342671(n)].

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j),

a(i) = a(j) => A372569(i) = A372569(j),

a(i) = a(j) => A372572(i) = A372572(j).

Links

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

Crossrefs

Cf. A009194, A009195, A009223, A322361, A342671.

Cf. also A305801, A372569, A372572.

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; };
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
Aux372570(n) = [gcd(n, sigma(n)), gcd(n, eulerphi(n)), gcd(eulerphi(n), sigma(n)), gcd(n, A003961(n)), gcd(sigma(n), A003961(n))];
v372570 = rgs_transform(vector(up_to, n, Aux372570(n)));
A372570(n) = v372570[n];