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A055940 Counterbalanced numbers: Composite n such that phi(n)/(sigma(n)-n) is an integer. 5
133, 403, 583, 713, 817, 2077, 2623, 2923, 4453, 4717, 5311, 5773, 7093, 7747, 9313, 11023, 11581, 11653, 12877, 14353, 15553, 19303, 20803, 21409, 21733, 21971, 24307, 31169, 35033, 39283, 39337, 43873, 46297, 46357, 50573, 50879, 53863 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

q=A000010(n)/A001065(n) is integer and n is composite.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000

Douglas E. Iannucci, On the Equation sigma(n) = n + phi(n), Journal of Integer Sequences, Vol. 20 (2017), Article 17.6.2.

EXAMPLE

n=133=7*19: phi(133)=108, sigma(133)-133=1+7+19=27, q=4

MATHEMATICA

Do[s=EulerPhi[n]/(DivisorSigma[1, n]-n); If[ !PrimeQ[n]&&IntegerQ[s], Print[n]], {n, 2, 1000000}]

PROG

(PARI) is(n)=!isprime(n) && n>1 && eulerphi(n)%(sigma(n)-n)==0 \\ Charles R Greathouse IV, Jan 02 2014

CROSSREFS

Cf. A000010, A001065, A068418, A020492, A070037.

Sequence in context: A064903 A259638 A070158 * A251131 A267288 A137879

Adjacent sequences:  A055937 A055938 A055939 * A055941 A055942 A055943

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jul 22 2000

STATUS

approved

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Last modified May 23 01:37 EDT 2019. Contains 323507 sequences. (Running on oeis4.)