A373528 Odd numbers k such that k, k+2 and k+4 all have at least two divisors with the same value of the Euler totient function (A000010).

4142435, 26196331, 77118741, 89690821, 102974571, 196054673, 201060275, 206568171, 277322153, 280039833, 401784953, 402492695, 415097613, 437290371, 515636303, 526721895, 534746581, 549806211, 575090395, 580329603, 625833871, 629588043, 702183625, 710983971, 716133481

Offset: 1

Author

Amiram Eldar, Jun 08 2024

Keywords

• nonn

Comments

Numbers k such that k, k+2 and k+4 are all in A359563.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Subsequence of A359563 and A373527.

Cf. A000010, A102190.

Programs

Mathematica

q[n_] := !UnsameQ @@ EulerPhi[Divisors[n]]; seq[kmax_] := Module[{tri = q /@ {1, 3, 5}, s = {}, k = 7}, While[k < kmax, If[And @@ tri, AppendTo[s, k - 6]]; tri = Join[Rest[tri], {q[k]}]; k+=2]; s]; seq[3*10^7]

PARI

is(k) = k>1 && k%2 && numdiv(k) > #Set(apply(x->eulerphi(x), divisors(k)));
lista(kmax) = {my(q1 = 0, q2 = 0, q3); forstep(k = 5, kmax, 2, q3 = is(k); if(q1 && q2 && q3, print1(k-4, ", ")); q1 = q2; q2 = q3);}