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A328954 Numbers m that are neither arithmetic (A003601) nor antiharmonic (A020487). 2
2, 8, 10, 12, 18, 24, 26, 28, 32, 34, 40, 48, 52, 58, 63, 72, 74, 75, 76, 80, 82, 84, 88, 90, 98, 104, 106, 108, 112, 120, 122, 124, 128, 130, 136, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178, 192, 194, 202, 208, 216, 218, 226, 228, 232, 234 (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 antiharmonic mean of the divisors of m is an integer.

Numbers m such that neither A(m) = A000203(m)/A000005(m) nor B(m) = A001157(m)/A000203(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, ...

Corresponding values of B(m): 5/3, 17/3, 65/9, 15/2, 35/3, 85/6, 425/21, 75/4, 65/3, 725/27, 221/9, ...

LINKS

Table of n, a(n) for n=1..57.

MATHEMATICA

Select[Range[235], !Divisible[DivisorSigma[2, #], (s = DivisorSigma[1, #])] && !Divisible[s, DivisorSigma[0, #]] &] (* Amiram Eldar, Dec 06 2019 *)

PROG

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

CROSSREFS

Cf. A000005, A000203, A001157, A003601, A277553, A328952, A328953.

Sequence in context: A287088 A296342 A328559 * A176969 A303358 A176464

Adjacent sequences:  A328951 A328952 A328953 * A328955 A328956 A328957

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Dec 03 2019

STATUS

approved

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Last modified March 7 18:54 EST 2021. Contains 341918 sequences. (Running on oeis4.)