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A328559 Numbers m that are neither arithmetic (A003601) nor squares (A000290). 2
2, 8, 10, 12, 18, 24, 26, 28, 32, 34, 40, 48, 50, 52, 58, 63, 72, 74, 75, 76, 80, 82, 84, 88, 90, 98, 104, 106, 108, 112, 117, 120, 122, 124, 128, 130, 136, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178, 180, 192, 194, 200, 202, 208, 216, 218, 226 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers m such that neither the arithmetic mean of the divisors of m nor the geometric mean of the divisors of m is an integer.

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

Corresponding values of A(m): 3/2, 15/4, 9/2, 14/3, 13/2, 15/2, 21/2, 28/3, 21/2, 27/2, 45/4, 62/5, 31/2, 49/3, 45/2, ...

Corresponding values of G(m): sqrt(2), sqrt(8), sqrt(10), sqrt(12), sqrt(18), sqrt(24), sqrt(26), sqrt(28), sqrt(32), ...

LINKS

Table of n, a(n) for n=1..58.

MATHEMATICA

Select[Range[230], !IntegerQ@Sqrt[#] && !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Nov 01 2019 *)

PROG

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

CROSSREFS

Cf. A000005, A000203, A000290, A003601, A328557, A328558.

Sequence in context: A297999 A287088 A296342 * A328954 A176969 A303358

Adjacent sequences:  A328556 A328557 A328558 * A328560 A328561 A328562

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Oct 31 2019

STATUS

approved

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Last modified February 26 14:41 EST 2021. Contains 341632 sequences. (Running on oeis4.)