A330746 Number of values of k, 1 <= k <= n, with A017666(k) = A017666(n), where A017666(n) = n/gcd(n, sigma(n)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 4, 1, 1, 3, 2, 1, 1, 1, 2, 1, 2, 1, 3, 1, 4, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 4, 1, 2, 1, 5, 1, 2, 1, 1, 1, 5, 1, 1, 3, 2, 1, 1, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 3, 1, 2, 3, 1, 1, 6, 4, 4, 1, 2, 4, 2, 1, 1, 1, 1, 1, 4, 1, 1, 3

Offset

1,6

Comments

Ordinal transform of A017666.

Links

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

Formula

For all n >= 1, a(A014567(n)) = 1.

For all n >= 1, a(A007691(n)) = a(A159907(n)) = a(A245775(n)) = n.

Prog

(PARI)
up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
A017666(n) = (n/gcd(n, sigma(n)));
v330746 = ordinal_transform(vector(up_to, n, A017666(n)));
A330746(n) = v330746[n];

Crossrefs

Cf. A009194, A014567, A017666.

A left inverse of following sequences: A007691, A159907, A245775.

Cf. also A331175.

Sequence in context: A051265 A008647 A036475 * A316555 A337531 A316556

Adjacent sequences: A330743 A330744 A330745 * A330747 A330748 A330749

Keyword

nonn

Author

Antti Karttunen, Jan 11 2020

Status

approved