A293184 Numbers k such that bphi(k) = bphi(k+1), where bphi(k) is the bi-unitary analog of Euler's totient function (A116550).

1, 14, 20, 57, 187, 188, 916, 1603, 93928, 142891, 432976, 549815, 692259, 773887, 872191, 4297168, 9478088, 127162432, 127991488, 129015616, 132527167

Offset

1,2

Comments

187 is the first solution to bphi(k) = bphi(k+1) = bphi(k+2).

a(22) > 1.6*10^9, if it exists. - Amiram Eldar, Jul 16 2022

Links

Table of n, a(n) for n=1..21.

Example

14 is in the sequence since bphi(14) = bphi(15) = 9.

Mathematica

bphi[1] = 1; bphi[n_] := With[{pp = Power @@@ FactorInteger[n]},   Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; a={}; b1=0; Do[b2 = bphi[k]; If[b1 == b2, a = AppendTo[a, k - 1]]; b1 = b2, {k, 1, 10^3}]; a (* after Jean-François Alcover at A116550 *)

Prog

(PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }
gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));
biuphi(n) = if (n==1, 1, sum(k=1, n-1, gcud(n, k) == 1));
isok(n) = biuphi(n) == biuphi(n+1);
lista(nn) = {x = biuphi(1); for (n=2, nn, y = biuphi(n); if (x==y, print1(n-1, ", ")); x = y; ); } \\ Michel Marcus, Nov 09 2017

Crossrefs

Cf. A001274, A116550, A287055, A294030.

Sequence in context: A259536 A067796 A015797 * A368408 A064974 A167335

Adjacent sequences: A293181 A293182 A293183 * A293185 A293186 A293187

Keyword

nonn,more

Author

Amiram Eldar, Oct 01 2017

Extensions

a(10) from Michel Marcus, Nov 11 2017

a(11) from Michel Marcus, Nov 12 2017

a(12)-a(21) from Amiram Eldar, Jul 16 2022

Status

approved