

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
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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 nT(n), where T(n) is the nth 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: A100933 A325128 A320056 * 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



