A344771 Ordinal transform of A342915, where A342915(n) = gcd(1+n, psi(n)).

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

Offset

1,4

Comments

Number of values of k, 1 <= k <= n, with A342915(k) = A342915(n).

a(p) = 1 for all primes p (and for some other numbers as well).

Links

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

Formula

a(n) <= A344773(n).

Mathematica

psi[n_] := If[n= 1, 1, Times@@((#1+1)*#1^(#2-1)& @@@ FactorInteger[n])];
A342915[n_] := GCD[n+1, psi[n]];
b[_] = 0;
a[n_] := a[n] = With[{t = A342915[n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 22 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; };
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
A342915(n) = gcd(1+n, A001615(n));
v344771 = ordinal_transform(vector(up_to, n, A342915(n)));
A344771(n) = v344771[n];

Crossrefs

Cf. A001615, A342915, A344773.

Differs from A339914 for the first time at n=44, where a(44) = 1, while A339914(44) = 8.

Sequence in context: A285324 A308551 A194550 * A339914 A242923 A065704

Adjacent sequences: A344768 A344769 A344770 * A344772 A344773 A344774

Keyword

nonn

Author

Antti Karttunen, May 31 2021

Status

approved