cp's OEIS Frontend

A175678 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.

%I A175678 #14 Oct 09 2023 12:53:00
%S A175678 1,6,14,20,22,30,38,42,44,46,54,56,60,62,66,68,70,78,86,92,94,96,102,
%T A175678 110,114,116,118,126,132,134,138,140,142,150,154,158,164,166,168,174,
%U A175678 182,184,186,188,190,198,204,206,210,212,214,220,222,224,230,236,238,246,248,254,258
%N A175678 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 A175678 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 A175678 {a(n)} = 1 and the even arithmetic numbers from A003601.
%C A175678 Subsequence of A003601.
%C A175678 Union of {a(n)} and A175679 = A003601 (arithmetic numbers).
%e A175678 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 A175678 (PARI) Ad(n) = sigma(n)/numdiv(n);
%o A175678 Ah(n) = if(n<2, n>0, n*eulerphi(n)/2)/eulerphi(n);
%o A175678 isok(k) = (type(Ad(k)) == "t_INT") && (type(Ah(k)) == "t_INT"); \\ _Michel Marcus_, Oct 09 2023
%Y A175678 Cf. A000203, A000005, A057020, A057021.
%Y A175678 CF. A023896, A000010, A026741, A040001.
%Y A175678 Cf. A003601, A175679.
%K A175678 nonn
%O A175678 1,2
%A A175678 _Jaroslav Krizek_, Aug 07 2010
%E A175678 More terms from _Michel Marcus_, Oct 09 2023