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A055468 Composite numbers for which Sum of EulerPhi and Divisor-Sum is an integer multiple of the 4th power of the number of divisors. 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
1,1
COMMENTS
Makowski proved that phi(n) + sigma(n) = n*d(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 by higher powers of the number of divisors.
REFERENCES
Sivaramakrishnan,R.(1989):Classical Theory of Arithmetical Functions Marcel Dekker,Inc., New York-Basel.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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
PROG
(PARI) is(n)=my(f=factor(n)); (eulerphi(f)+sigma(f))%numdiv(f)^4==0 && !isprime(n) \\ Charles R Greathouse IV, Mar 01 2017
CROSSREFS
Sequence in context: A137850 A262517 A036231 * A134328 A113614 A134941
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 27 2000
STATUS
approved

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Last modified February 24 17:27 EST 2024. Contains 370307 sequences. (Running on oeis4.)