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A326713 Numbers m that are neither arithmetic (A003601) nor RMS numbers (A140480). 0
2, 4, 8, 9, 10, 12, 16, 18, 24, 25, 26, 28, 32, 34, 36, 40, 48, 50, 52, 58, 63, 64, 72, 74, 75, 76, 80, 81, 82, 84, 88, 90, 98, 100, 104, 106, 108, 112, 117, 120, 121, 122, 124, 128, 130, 136, 144, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers m such that neither A(m) = A000203(m) / A000005(m) nor Q(m) = sqrt(A001157(m) / A000005(m)) is an integer.

Numbers m such that neither A(m) = A000203(m) / A000005(m) nor Q(m) = sqrt(A001157(m) / A000005(m)) is an integer.

Corresponding values of A(m): 3/2, 7/3, 15/4, 13/3, 9/2, 14/3, 31/5, 13/2, 15/2, 31/3, 21/2, 28/3, 21/2, 27/2, 91/9, 45/4, ...

Corresponding values of Q(m): sqrt(5/2), sqrt(7), sqrt(85/4), sqrt(91/3), sqrt(65/2), sqrt(35), sqrt(341/5), sqrt(455/6), ...

Sequence deviates from A049642; number 2217231104 (the first RMS number that is not arithmetic) is a term of A049642 but is not a term of this sequence.

LINKS

Table of n, a(n) for n=1..59.

MATHEMATICA

Select[Range[178], !IntegerQ @ RootMeanSquare[Divisors[#]] && !Divisible[ DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Oct 20 2019 *)

PROG

(MAGMA) [m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(&+[d^2: d in Divisors(m)] / NumberOfDivisors(m)))]

CROSSREFS

Cf. A000005, A000203, A001157, A003601, A049642, A140480, A327055.

Sequence in context: A003485 A072602 A049642 * A328945 A050907 A100675

Adjacent sequences:  A326710 A326711 A326712 * A326714 A326715 A326716

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Oct 18 2019

STATUS

approved

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Last modified July 15 02:31 EDT 2020. Contains 335762 sequences. (Running on oeis4.)