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.

1, 6, 14, 20, 22, 30, 38, 42, 44, 46, 54, 56, 60, 62, 66, 68, 70, 78, 86, 92, 94, 96, 102, 110, 114, 116, 118, 126, 132, 134, 138, 140, 142, 150, 154, 158, 164, 166, 168, 174, 182, 184, 186, 188, 190, 198, 204, 206, 210, 212, 214, 220, 222, 224, 230, 236, 238, 246, 248, 254, 258

Offset: 1

Author

Jaroslav Krizek, Aug 07 2010

Keywords

• nonn

Comments

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.

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

Subsequence of A003601.

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

Examples

			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.
		

Crossrefs

Cf. A000203, A000005, A057020, A057021.

CF. A023896, A000010, A026741, A040001.

Cf. A003601, A175679.

Programs

PARI

Ad(n) = sigma(n)/numdiv(n);
Ah(n) = if(n<2, n>0, n*eulerphi(n)/2)/eulerphi(n);
isok(k) = (type(Ad(k)) == "t_INT") && (type(Ah(k)) == "t_INT"); \\ Michel Marcus, Oct 09 2023

Extensions

More terms from Michel Marcus, Oct 09 2023