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

1,2

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

Links

Table of n, a(n) for n=1..26.

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A338422 A171885 A331261 * A039583 A042123 A041531

Adjacent sequences: A063983 A063984 A063985 * A063987 A063988 A063989

Keyword

nonn

Author

Labos Elemer, Sep 06 2001

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

Status

approved