This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A055468 Composite numbers for which Sum of EulerPhi and Divisor-Sum is an integer multiple of the 4th power of the number of divisors. 0
 1, 121, 125, 511, 767, 895, 1535, 1919, 2047, 2559, 2815, 3071, 3199, 3327, 3455, 3711, 3839, 4223, 4351, 4479, 4607, 4735, 4863, 5262, 5631, 5726, 5759, 5902, 5966, 6014, 6527, 7167, 7295, 7423, 7679, 7807, 8063, 9599, 9727, 9819, 9983, 10239 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Makowski proved that phi(n)+Sigma[n] = nd[n] iff n is a prime (see in Sivaramakrishnan,Chapter I, page 8, Theorem 3) In more special cases k differs from n and Phi+Sigma is divisible with higher powers of the number of divisors REFERENCES Sivaramakrishnan,R.(1989):Classical Theory of Arithmetical Functions Marcel Dekker,Inc., New York-Basel. LINKS FORMULA Integer solutions of Phi[x]+Sigma[x] = kd[x]^4 or A000203(n)+A000010(n) = k*A000005(n)^4, where k is integer. EXAMPLE n = 511 with 4 divisors,Sigma(511) = 592, Phi(511) = 432, 592+432 = 1024 = k*4^4, where k = 4 CROSSREFS Sequence in context: A014735 A137850 A036231 * A134328 A113614 A134941 Adjacent sequences:  A055465 A055466 A055467 * A055469 A055470 A055471 KEYWORD nonn AUTHOR Labos E. (labos(AT)ana.sote.hu), Jun 27 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .