A354990 Ordinal transform of A344005, where A344005(n) is the smallest positive integer m such that n divides m*(m+1).

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

Offset: 1

Author

Antti Karttunen, Jun 17 2022

Keywords

• nonn

Comments

Number of values of k, 1 <= k <= n, with A344005(k) = A344005(n).

Links

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

Crossrefs

Cf. A344005, A354991.

Cf. also A344770, A345934.

Programs

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; };
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
v354990 = ordinal_transform(vector(up_to,n,A344005(n)));
A354990(n) = v354990[n];

Formula

a(n) >= A354991(n).