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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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. a(n) = odd arithmetic numbers from A003601. Subsequence of A003601. Union a(n) and A175678(n+1) = A003601(n) (arithmetic numbers).

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

Only odd numbers are possible members since 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 members: 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: A245644 A070087 A100933 * A088828 A182318 A247424

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

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Last modified September 20 06:59 EDT 2018. Contains 315226 sequences. (Running on oeis4.)