

A015707


Values of n where (phi(n) * sigma(n))/n is an integer and increases.


0



1, 6, 18, 24, 28, 40, 54, 72, 96, 117, 135, 196, 200, 216, 224, 288, 360, 384, 468, 496, 600, 640, 756, 775, 864, 891, 1000, 1080, 1152, 1372, 1488, 1521, 1568, 1701, 1792, 1944, 2016, 2160, 2176, 2480, 2592, 3100, 3159, 3200, 3375, 3456, 3744, 4320, 4455, 4608
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OFFSET

1,2


COMMENTS

This sequence is infinite since there are infinitely many numbers m with an arbitrarily large integer value of (phi(m) * sigma(m))/m. For example, if m = 2 * 3^k, then this value is (3^(k+1)1)/2.  Amiram Eldar, Dec 05 2018


LINKS

Table of n, a(n) for n=1..50.
Richard K. Guy, Divisors and desires, Amer. Math. Monthly, 104 (1997), 359360.


MATHEMATICA

seq = {}; rm = 0; Do[r = EulerPhi[n]*DivisorSigma[1, n]/n; If[IntegerQ[r] && r > rm, rm = r; AppendTo[seq, n]], {n, 1, 5000}]; seq (* Amiram Eldar, Dec 05 2018 *)


CROSSREFS

Cf. A015706.
Sequence in context: A275168 A236359 A011775 * A236864 A101527 A028887
Adjacent sequences: A015704 A015705 A015706 * A015708 A015709 A015710


KEYWORD

nonn


AUTHOR

Robert G. Wilson v


EXTENSIONS

Title improved by Sean A. Irvine, Dec 05 2018
a(1)=1 inserted and more terms added by Amiram Eldar, Dec 05 2018


STATUS

approved



