A344773 -id:A344773 - cp's OEIS frontend

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

Antti Karttunen, May 31 2021

nonn

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).

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

Cf. A001615, A342915, A344773.

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

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 *)

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];

a(n) <= A344773(n).

A344774 Number of divisors d of n for which A049559(d) = A049559(n), where A049559(n) = gcd(n-1, phi(n)).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, May 31 2021

nonn

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

Cf. A000010, A049559, A330747.

Cf. also A344773.

A049559(n) = gcd(n-1, eulerphi(n));
A344774(n) = { my(x=A049559(n)); sumdiv(n,d,A049559(d)==x); };

a(n) = Sum_{d|n} [A049559(d) = A049559(n)], where [ ] is the Iverson bracket.

a(n) <= A330747(n).

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula