A175678 - OEIS

%I #14 Oct 09 2023 12:53:00

%S 1,6,14,20,22,30,38,42,44,46,54,56,60,62,66,68,70,78,86,92,94,96,102,

%T 110,114,116,118,126,132,134,138,140,142,150,154,158,164,166,168,174,

%U 182,184,186,188,190,198,204,206,210,212,214,220,222,224,230,236,238,246,248,254,258

%N Numbers m such that the arithmetic mean Ad(m) of the divisors of m and the arithmetic mean Ah(m) of the numbers h < m such that gcd(h,m) = 1 are both integer.

%C Numbers m such that Ad(m) = A000203(m)/A000005(m) = A057020(m)/A057021(m) and Ah(m) = A023896(m)/A000010(m) = A026741(m)/A040001(m-1) are both integers.

%C {a(n)} = 1 and the even arithmetic numbers from A003601.

%C Subsequence of A003601.

%C Union of {a(n)} and A175679 = A003601 (arithmetic numbers).

%e a(2) = 6, Ad(6) = (1+2+3+6)/4 = 3, Ah(6) = (1+5)/2 = 3, Ad(6) and Ah(6) are both integer.

%o (PARI) Ad(n) = sigma(n)/numdiv(n);

%o Ah(n) = if(n<2, n>0, n*eulerphi(n)/2)/eulerphi(n);

%o isok(k) = (type(Ad(k)) == "t_INT") && (type(Ah(k)) == "t_INT"); \\ _Michel Marcus_, Oct 09 2023

%Y Cf. A000203, A000005, A057020, A057021.

%Y CF. A023896, A000010, A026741, A040001.

%Y Cf. A003601, A175679.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Aug 07 2010

%E More terms from _Michel Marcus_, Oct 09 2023