A372572 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j), A322361(i) = A322361(j) and A342671(i) = A342671(j), for all i, j >= 1.

1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 1, 5, 1, 4, 6, 1, 1, 7, 1, 8, 1, 4, 1, 9, 1, 4, 10, 11, 1, 12, 1, 13, 14, 4, 15, 16, 1, 4, 1, 17, 1, 3, 1, 18, 6, 4, 1, 5, 1, 2, 14, 19, 1, 20, 1, 21, 10, 4, 1, 22, 1, 4, 1, 1, 23, 3, 1, 24, 14, 25, 1, 26, 1, 4, 27, 28, 29, 3, 1, 4, 1, 4, 1, 30, 1, 4, 31, 32, 1, 33, 34, 18, 1, 4, 35, 36, 1, 2, 37, 23

Offset

1,2

Comments

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

For all i, j:

a(i) = a(j) => A349167(i) = A349167(j),

a(i) = a(j) => A353666(i) = A353666(j),

a(i) = a(j) => A372565(i) = A372565(j).

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Prog

(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); };
Aux372572(n) = [gcd(n, sigma(n)), gcd(n, A003961(n)), gcd(sigma(n), A003961(n))];
v372572 = rgs_transform(vector(up_to, n, Aux372572(n)));
A372572(n) = v372572[n];

Crossrefs

Cf. A009194, A322361, A342671, A349167, A353666, A372565.

Sequence in context: A360615 A280274 A073408 * A120454 A321648 A330755

Adjacent sequences: A372569 A372570 A372571 * A372573 A372574 A372575

Keyword

nonn

Author

Antti Karttunen, May 24 2024

Status

approved