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

1,1

Comments

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

Links

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

Example

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.

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]

Prog

(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))));

Crossrefs

Cf. A064380.

Similar sequences: A007694, A097296, A319481, A335327.

Sequence in context: A299381 A247984 A108417 * A185078 A214402 A166064

Adjacent sequences: A373054 A373055 A373056 * A373058 A373059 A373060

Keyword

nonn

Author

Amiram Eldar, May 21 2024

Status

approved