A344770 Ordinal transform of A011772.

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

Offset

1,6

Comments

Number of values of k, 1 <= k <= n, with A011772(k) = A011772(n).

a(n) = 1 for all powers of primes, A000961. Ones occur on some other positions as well: 15, 22, 35, 38, 42, 44, 45, 46, 51, 52, 54, 65, ...

Links

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

Formula

a(n) >= A344590(n).

Mathematica

A011772[n_] := For[m = 1, True, m++, If[Divisible[m(m+1)/2, n], Return[m]]];
b[_] = 0;
a[n_] := a[n] = With[{t = A011772[n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 21 2021 *)

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; };
A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
v344770 = ordinal_transform(vector(up_to, n, A011772(n)));
A344770(n) = v344770[n];

Crossrefs

Cf. A000961, A011772, A344590.

Sequence in context: A124766 A359233 A337323 * A293895 A300385 A317145

Adjacent sequences: A344767 A344768 A344769 * A344771 A344772 A344773

Keyword

nonn,look

Author

Antti Karttunen, May 30 2021

Status

approved