A116518 -id:A116518 - cp's OEIS frontend

A070418 Numbers k such that k and phi(k) have the same number of divisors.

1, 3, 14, 15, 22, 28, 44, 46, 50, 56, 68, 70, 78, 88, 92, 94, 110, 112, 118, 166, 174, 176, 184, 188, 198, 214, 224, 228, 230, 234, 236, 255, 260, 294, 306, 318, 332, 334, 342, 352, 358, 368, 376, 414, 428, 448, 454, 462, 470, 472, 492, 500, 526, 550, 580, 590

Offset: 1

Benoit Cloitre, May 12 2002

This is an infinite sequence; for example, 2^(m-1)*5^m is in the sequence for all m >= 2. See Bellaouar et al. 2023. - Allen Stenger, Feb 16 2024

G. C. Greubel, Table of n, a(n) for n = 1..8407 (for values up to 500000)
Djamel Bellaouar, Abdelmadjid Boudaoud and Rafael Jakimczuk, Notes on the equation d(n) = d(phi(n)) and related inequalities, Math. Slovaca 73 (2023), no. 3, 613-632.

Cf. A000005, A000010 (phi), A116518 (odd terms).

Select[Range[600],DivisorSigma[0,#]==DivisorSigma[0,EulerPhi[#]]&] (* Harvey P. Dale, Sep 04 2015 *)

for(n=1,900,if(numdiv(n)==numdiv(eulerphi(n)),print1(n,",")))

A250405 Numbers k such that all values of Euler phi (A000010) of all divisors of k are pairwise distinct and represent all proper divisors of k+1.

Original entry on oeis.org

1, 3, 15, 255, 65535, 4294967295

Offset: 1

Jaroslav Krizek, Nov 22 2014

Numbers k such that {phi(d) : d|k} = {d : d|(k+1), d<(k+1)} as multisets.
Conjecture: last term is 4294967295.
First six terms coincide with A051179. - Omar E. Pol, Apr 12 2025

			15 is in the sequence because {phi(d) : d|15} = {1, 2, 4, 8} = {d : d|16, d<16}.
2 is not in the sequence because {phi(d) : d|2} = {1, 1}, but {d : d|2, d<2} = {1}.

Subsequence of A250404 and A203966.
Sequence differs from A051179, A050474 and A116518.
Cf. A000010.

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

Edited and a(6) added by Max Alekseyev, May 04 2024

cp's OEIS Frontend

A070418 Numbers k such that k and phi(k) have the same number of divisors.

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