A063986 Numbers k that divide Sum_{j=1..k} A051953(j) where A051953(j) = j - Phi(j). Arithmetic mean of first k cototient values is an integer.

1, 4, 5, 24, 25, 249, 600, 617, 12272, 13763, 21332, 25228, 783665, 15748051, 41846733, 195853251, 2488541984, 14399065016, 21119309213, 22430204140, 43787603128, 157825075944, 206651865067, 271605149320, 374049315076, 650288309748

Offset: 1

Author

Labos Elemer, Sep 06 2001

Keywords

• nonn

Comments

The odd terms of A048290 and A063986 are the same. - Jud McCranie, Jun 26 2005

a(27) > 10^12. - Donovan Johnson, Dec 09 2011

Examples

			k=5: (1 + 1 + 2 + 2 + 4)/5 = 2.
		

Crossrefs

Cf. A051953, A000010, A002088, A048920, A000217, A050226.

Programs

Mathematica

s = 0; Do[s = s + n - EulerPhi[n]; If[ IntegerQ[s/n], Print[n]], {n, 1, 10^7} ]

Extensions

More terms from Dean Hickerson, Sep 07 2001

One more term from Robert G. Wilson v, Sep 07 2001

a(16) and a(17) from Jud McCranie, Jun 22 2005

a(18)-a(21) from Donovan Johnson, May 11 2010

a(22)-a(26) from Donovan Johnson, Dec 09 2011