A373057 Numbers k such that iphi(k) divides k, where iphi is the infinitary Euler phi function (A064380).

2, 6, 8, 10, 60, 70, 120, 128, 136, 9822, 18632, 32768, 32896, 36720, 69726, 73662, 73686, 73734, 85962, 86046, 87114, 87198, 87222, 87258, 87294, 87306, 87342, 87366, 87546, 87558, 88014, 88278, 88302, 88338, 88386, 127326, 128046, 128082, 128382, 128406, 128598

Offset: 1

Author

Amiram Eldar, May 21 2024

Keywords

• nonn

Comments

Numbers k such that the number of numbers less than k that are infinitarily relatively prime to k is a divisor of k.

Examples

			2 is a term since ipghi(2) = 1 divides 2.
6 is a term since ipghi(6) = 6 divides 6.
60 is a term since ipghi(60) = 30 divides 60.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..218

Crossrefs

Cf. A064380.

Similar sequences: A007694, A097296, A319481, A335327.

Programs

Mathematica

infCoprimeQ[n1_, n2_] := Module[{g = GCD[n1, n2]}, If[g == 1, True, AllTrue[ FactorInteger[g][[;; , 1]], BitAnd @@ IntegerExponent[{n1, n2}, #] == 0 &]]]; q[n_] := Divisible[n, Sum[Boole[infCoprimeQ[j, n]], {j, 1, n-1}]]; Select[Range[2, 200], q]

PARI

isinfcoprime(n1, n2) = {my(g = gcd(n1, n2), p, e1, e2); if(g == 1, return(1)); p = factor(g)[, 1]; for(i=1, #p, e1 = valuation(n1, p[i]); e2 = valuation(n2, p[i]); if(bitand(e1, e2) > 0, return(0))); 1; }
is(n) = if(n < 2, 0, !(n % sum(j = 1, n-1, isinfcoprime(j, n))));