A303755 -id:A303755 - cp's OEIS frontend

A303756 Number of values of k, 1 <= k <= n, with A002322(k) = A002322(n), where A002322 is Carmichael lambda.

1, 2, 1, 2, 1, 3, 1, 4, 2, 2, 1, 5, 1, 3, 3, 4, 1, 4, 1, 5, 5, 2, 1, 6, 1, 2, 2, 6, 1, 6, 1, 1, 3, 2, 3, 7, 1, 3, 4, 7, 1, 8, 1, 4, 5, 2, 1, 8, 2, 2, 3, 6, 1, 4, 3, 9, 5, 2, 1, 9, 1, 2, 10, 4, 7, 5, 1, 5, 3, 8, 1, 11, 1, 2, 4, 6, 3, 9, 1, 10, 1, 2, 1, 12, 6, 3, 3, 6, 1, 10, 11, 4, 4, 2, 3, 2, 1, 4, 5, 5, 1, 7, 1, 12, 13

Offset: 1

Antti Karttunen, Apr 30 2018

nonn

Ordinal transform of A002322.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A002322.

Cf. also A081373, A303755, A303758.

a[n_] := With[{c = CarmichaelLambda[n]}, Select[Range[n], c == CarmichaelLambda[#]&] // Length];
Array[a, 1000] (* Jean-François Alcover, Sep 19 2020 *)

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; };
A002322(n) = lcm(znstar(n)[2]); \\ From A002322
v303756 = ordinal_transform(vector(up_to,n,A002322(n)));
A303756(n) = v303756[n];

Except for a(2) = 2, a(n) = A303758(n).

A322025 Ordinal transform of A322023.

Original entry on oeis.org

1, 1, 2, 2, 3, 1, 4, 1, 3, 1, 5, 1, 6, 2, 1, 2, 7, 1, 8, 1, 1, 4, 9, 1, 10, 2, 5, 2, 11, 1, 12, 1, 1, 3, 2, 1, 13, 3, 3, 1, 14, 1, 15, 1, 2, 6, 16, 1, 7, 1, 3, 3, 17, 2, 2, 1, 2, 8, 18, 1, 19, 9, 1, 4, 1, 1, 20, 3, 4, 2, 21, 1, 22, 2, 2, 2, 3, 1, 23, 1, 24, 3, 25, 1, 1, 4, 5, 3, 26, 1, 1, 5, 3, 10, 5, 1, 27, 3, 2, 1, 28, 1, 29, 1, 1

Offset: 1

Antti Karttunen, Dec 01 2018

nonn

Positions where 1, 2, 3, 4, 5, ... occur for the first time are 1, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 187, 191, 193, ... Note that this is not a subsequence of A000961; for example, 187 = 11*17 is a semiprime.

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

Cf. A000010, A002322, A081373, A303753, A303755, A303756, A303777, A322023.

\\ Needs also code from A322023.
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; };
v322025 = ordinal_transform(v322023);
A322025(n) = v322025[n];

cp's OEIS Frontend

A303756 Number of values of k, 1 <= k <= n, with A002322(k) = A002322(n), where A002322 is Carmichael lambda.

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