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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.
6

%I #22 Aug 20 2021 22:48:57

%S 1,4,5,24,25,249,600,617,12272,13763,21332,25228,783665,15748051,

%T 41846733,195853251,2488541984,14399065016,21119309213,22430204140,

%U 43787603128,157825075944,206651865067,271605149320,374049315076,650288309748

%N 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.

%C The odd terms of A048290 and A063986 are the same. - _Jud McCranie_, Jun 26 2005

%C a(27) > 10^12. - _Donovan Johnson_, Dec 09 2011

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

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

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

%K nonn

%O 1,2

%A _Labos Elemer_, Sep 06 2001

%E More terms from _Dean Hickerson_, Sep 07 2001

%E One more term from _Robert G. Wilson v_, Sep 07 2001

%E a(16) and a(17) from _Jud McCranie_, Jun 22 2005

%E a(18)-a(21) from _Donovan Johnson_, May 11 2010

%E a(22)-a(26) from _Donovan Johnson_, Dec 09 2011