A121249 - OEIS

%I #16 Apr 07 2019 10:43:27

%S 6,90,495,570,735,1530,3630,4235,4466,6045,6622,7595,13035,17745,

%T 22165,22425,23275,27195,42826,61915,71445,75690,76615,77418,77714,

%U 81466,94575,103334,105945,117502,122486,175714,214038,245985,330315,349410,357357,378235

%N Larger members of primitive phi-amicable pairs.

%C A phi-amicable pair (a0,a1) with 1<a0<=a1 satisfies phi(a0)=phi(a1)=(a0+a1)/k for some integer k>=1. Table contains a subset of primitive pairs that are a form of smallest generators for more phi-amicable pairs as defined in the reference.

%C A pair is called primitive if there is no common divisor g > 1 of a0 and a1 such that (a0/g, a1/g) is also phi-amicable. - _Amiram Eldar_, Apr 06 2019

%H Amiram Eldar, <a href="/A121249/b121249.txt">Table of n, a(n) for n = 1..499</a> (terms below 10^9)

%H Graeme L. Cohen and Herman te Riele, <a href="https://ir.cwi.nl/pub/4921">On phi-amicable pairs (with appendix)</a>, Research Report R95-9 (December 1995), School of Mathematical Sciences, University of Technology, Sydney, and CWI-Report NM-R9524 (November 1995), CWI Amsterdam.

%H Graeme L. Cohen and Herman te Riele, <a href="https://doi.org/10.1090/S0025-5718-98-00933-8">On phi-amicable pairs</a>, Mathematics of Computation, Vol. 67, No. 221 (1998), pp. 399-411.

%H Amiram Eldar, <a href="/A121249/a121249.txt">Table of n, a0(n), a1(n) for n=1..499</a> (from Cohen & te Riele 1995)

%t aQ[m_, n_] := (e = EulerPhi[m]) == EulerPhi[n] && Divisible[m + n, e]; paQ[m_, n_] := aQ[m, n] && Module[{g = GCD[m, n], ans = True}, d = Divisors[g]; Do[d1 = d[[k]]; If[aQ[m/d1, n/d1], ans = False; Break[]], {k, 2, Length[d]}]; ans]; seqQ[n_] := Module[{k = 2}, While[k < n && ! paQ[k, n], k++]; k < n]; Select[Range[1000], seqQ] (* _Amiram Eldar_, Apr 06 2019 *)

%Y Cf. A000010.

%K nonn

%O 1,1

%A _R. J. Mathar_, Sep 06 2006