A123728 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.

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

Offset

1,1

Comments

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

R. J. Mathar did an exhaustive search up to 2000.

Giovanni Resta searched up to 10^7.

Links

Table of n, a(n) for n=1..12.

Example

Kohmoto found the following terms.
k=3:
m=2^9*3*31*1021*7*23 n=2^9*3*31*1021*191
m=2^5*3*61*5*11 n=2^5*3*61*71
m=2^8*7*37*73*509*3*5 n=2^8*7*37*73*509*23
m=2^8*7*19*37*73*509*3*11 n=2^8*7*19*37*73*509*47
m=2^8*5*7*37*73*509*11*59 n=2^8*5*7*37*73*509*719
k=2:
m=2*3^2*5*13*23*29 n=2*3^2*5*13*719
m=2^2*7*3*11 n=2^2*7*47
m=3^2*5^2*13*29*17*19 n=3^2*5^2*13*29*359
k=5:
m=2^5*3^2*7*13*61*23*29 n=2^5*3^2*7*13*61*719
m=2^9*3^2*11*13*31*1021*23*29 n=2^9*3^2*11*13*31*1021*719

Crossrefs

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

Sequence in context: A335388 A123729 A193835 * A193876 A293124 A193185

Adjacent sequences: A123725 A123726 A123727 * A123729 A123730 A123731

Keyword

nonn,more

Author

Yasutoshi Kohmoto, Nov 18 2006

Status

approved