

A055467


Composite numbers for which Sum of EulerPhi and DivisorSum is an integer multiple of the cube of the number of divisors.


0



1, 95, 99, 121, 125, 159, 287, 319, 415, 447, 511, 543, 654, 671, 703, 767, 799, 831, 895, 959, 1055, 1119, 1247, 1343, 1390, 1495, 1535, 1631, 1727, 1849, 1919, 1983, 2043, 2047, 2060, 2261, 2271, 2335, 2463, 2495, 2559, 2623, 2815, 2828, 2883, 2911
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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 YorkBasel.


LINKS

Table of n, a(n) for n=1..46.


FORMULA

Integer solutions of Phi[x]+Sigma[x] = kd[x]^3 or A000203(n)+A000010(n) = k*A000005(n)^3, where k is integer.


EXAMPLE

n = 95 with 4 divisors,Sigma(95) = 120, Phi(95) = 72 72+120 = 192 = 3*4*4*4, k = 3


CROSSREFS

A000005, A000010, A000203.
Sequence in context: A033415 A067266 A171403 * A057654 A181767 A046005
Adjacent sequences: A055464 A055465 A055466 * A055468 A055469 A055470


KEYWORD

nonn


AUTHOR

Labos Elemer, Jun 27 2000


STATUS

approved



