A175679 Numbers m such that arithmetic mean Ad(m) of divisors of m and arithmetic mean Ak(m) of numbers 1 <= k <= m are both integer.

1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 119, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141

Offset

1,2

Comments

Numbers m such that Ad(m) = A000203(m) / A000005(m) = A057020(m) / A057021(m) and Ak(m) = A000217(m) / A000027(m) = A145051(m) / A040001(m) are both integer.

Subsequence of A003601: {a(n)} = odd arithmetic numbers from A003601.

{a(n)} union A175678 = A003601 (arithmetic numbers).

From Robert G. Wilson v, Aug 09 2010: (Start)

All terms are odd because the second criterion is equivalent to n|T(n), where T(n) is the n-th triangular number, A000217(n).

Terms that are not prime are 1, 15, 21, 27, 33, 35, 39, 45, 49, 51, 55, 57, 65, 69, 77, 85, ..., .

Odd integers that are not terms: 9, 25, 63, 75, 81, 117, 121, 171, 175, 225, 243, 279, 289, ..., . (End)

Links

Table of n, a(n) for n=1..64.

Example

a(4) = 7, Ad(7) = (1+7)/2 = 4, Ak(7) = (1+2+3+4+5+6+7)/7 = 4, Ad(7) and Ak(7) are both integer.

Mathematica

fQ[n_] := OddQ@n && Mod[DivisorSigma[1, n], DivisorSigma[0, n]] == 0; Select[ Range@ 142, fQ] (* Robert G. Wilson v, Aug 09 2010 *)

Crossrefs

Sequence in context: A352830 A380694 A320056 * A088828 A348741 A348748

Adjacent sequences: A175676 A175677 A175678 * A175680 A175681 A175682

Keyword

nonn

Author

Jaroslav Krizek, Aug 07 2010

Extensions

More terms from Robert G. Wilson v, Aug 09 2010

Status

approved