A248795 Numbers k such that Product_{d|k} phi(d) = Product_{d|(k+1)} phi(d) where phi(x) = Euler totient function (A000010).

1, 3, 5, 15, 255, 65535, 2200694, 2619705, 6372794, 40588485, 76466985, 81591194, 118018094, 206569605, 470542485, 525644385, 726638834, 791937614, 971122514, 991172805, 1268457014, 1384822005, 1613055045, 1709460753, 1861556654, 1872619665, 2507927414, 2659263945

Offset: 1

Author

Jaroslav Krizek, Nov 19 2014

Keywords

• nonn

Comments

Numbers k such that A029940(k) = A029940(k+1).

4294967295 is in this sequence.

Examples

			15 is in the sequence because A029940(15) = A029940(16) = 64.
		

Crossrefs

Cf. A000010, A019434, A029940, A248796.

Programs

Magma

[n: n in [1..100000] | (&*[EulerPhi(d): d in Divisors(n)]) eq (&*[EulerPhi(d): d in Divisors(n+1)])];

Mathematica

a248795[n_Integer] := Select[Range[n],
Product[EulerPhi[i], {i, Divisors[#]}] ==
Product[EulerPhi[j], {j, Divisors[# + 1]}] &]; a248795[10^5] (* Michael De Vlieger, Nov 30 2014 *)

PARI

lista(nn) = {d = divisors(1); vcur = prod(k=1, #d, eulerphi(d[k])); for (n=2, nn, d = divisors(n); vnext = prod(k=1, #d, eulerphi(d[k])); if (vnext == vcur, print1(n-1, ", ")); vcur = vnext;);} \\ Michel Marcus, Nov 23 2014

Formula

a(n) = A248796(n) - 2.

Extensions

a(7)-a(9) from Michel Marcus, Nov 21 2014

a(10)-a(20) from Michel Marcus, Nov 23 2014

More terms from Jinyuan Wang, Jul 27 2025