A123728 - OEIS

%I #8 Jan 24 2019 03:56:28

%S 6,140,1316,1560,14384,18018,23562,40992,94188,141128,168730,187652

%N Call (m,n) a "(-1)SSU amicable pair" if (-1)Sigma(m)*Sigma(m) = k*UnitaryPhi(m)*(m+n) and (-1)Sigma(n)*Sigma(n) = k*UnitaryPhi(n)*(m+n) for some integer k. Sequence gives values of m, assuming n <= m.

%C a(3) is an example with m != n.

%C _R. J. Mathar_ did an exhaustive search up to 2000.

%C _Giovanni Resta_ searched up to 10^7.

%e Kohmoto found the following terms.

%e k=3:

%e m=2^9*3*31*1021*7*23 n=2^9*3*31*1021*191

%e m=2^5*3*61*5*11 n=2^5*3*61*71

%e m=2^8*7*37*73*509*3*5 n=2^8*7*37*73*509*23

%e m=2^8*7*19*37*73*509*3*11 n=2^8*7*19*37*73*509*47

%e m=2^8*5*7*37*73*509*11*59 n=2^8*5*7*37*73*509*719

%e k=2:

%e m=2*3^2*5*13*23*29 n=2*3^2*5*13*719

%e m=2^2*7*3*11 n=2^2*7*47

%e m=3^2*5^2*13*29*17*19 n=3^2*5^2*13*29*359

%e k=5:

%e m=2^5*3^2*7*13*61*23*29 n=2^5*3^2*7*13*61*719

%e m=2^9*3^2*11*13*31*1021*23*29 n=2^9*3^2*11*13*31*1021*719

%Y Cf. A123729 (values of n), A123582 (values of k).

%K nonn,more

%O 1,1

%A _Yasutoshi Kohmoto_, Nov 18 2006