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

1,2

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).

Links

Table of n, a(n) for n=1..61.

Example

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.

Prog

(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

Crossrefs

Cf. A000203, A000005, A057020, A057021.

CF. A023896, A000010, A026741, A040001.

Cf. A003601, A175679.

Sequence in context: A351975 A255217 A048747 * A173870 A101567 A123267

Adjacent sequences: A175675 A175676 A175677 * A175679 A175680 A175681

Keyword

nonn

Author

Jaroslav Krizek, Aug 07 2010

Extensions

More terms from Michel Marcus, Oct 09 2023

Status

approved