A121249 Larger members of primitive phi-amicable pairs.

6, 90, 495, 570, 735, 1530, 3630, 4235, 4466, 6045, 6622, 7595, 13035, 17745, 22165, 22425, 23275, 27195, 42826, 61915, 71445, 75690, 76615, 77418, 77714, 81466, 94575, 103334, 105945, 117502, 122486, 175714, 214038, 245985, 330315, 349410, 357357, 378235

Offset

1,1

Comments

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.

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..499 (terms below 10^9)

Graeme L. Cohen and Herman te Riele, On phi-amicable pairs (with appendix), Research Report R95-9 (December 1995), School of Mathematical Sciences, University of Technology, Sydney, and CWI-Report NM-R9524 (November 1995), CWI Amsterdam.

Graeme L. Cohen and Herman te Riele, On phi-amicable pairs, Mathematics of Computation, Vol. 67, No. 221 (1998), pp. 399-411.

Amiram Eldar, Table of n, a0(n), a1(n) for n=1..499 (from Cohen & te Riele 1995)

Mathematica

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 *)

Crossrefs

Cf. A000010.

Sequence in context: A177568 A177573 A166782 * A113404 A177283 A121607

Adjacent sequences: A121246 A121247 A121248 * A121250 A121251 A121252

Keyword

nonn

Author

R. J. Mathar, Sep 06 2006

Status

approved