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A325020
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Numbers m such that m*(m-tau(m))/sigma(m) is an integer h where k-tau(k) is the number of nondivisors of k (A049820) and sigma(k) is the sum of the divisors of k (A000203).
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4
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1, 2, 6, 22, 28, 76, 84, 90, 96, 170, 216, 248, 252, 496, 520, 532, 588, 672, 700, 852, 864, 1240, 2176, 2448, 2480, 2812, 3360, 6048, 7392, 7584, 8128, 9120, 11480, 12616, 12768, 13832, 14056, 14720, 15456, 19488, 20536, 21216, 27000, 30240, 31584, 31968
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OFFSET
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1,2
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COMMENTS
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Even perfect numbers from A000396 are terms.
Corresponding values of integers h: 0, 0, 1, 11, 11, 38, 27, 30, 32, 85, 72, 124, 81, ...
Supersequence of A325021 and A325023.
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LINKS
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Table of n, a(n) for n=1..46.
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EXAMPLE
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28 is a term because 28*(28-tau(28))/sigma(28) = 28*(28-6)/56 = 11 (integer).
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MATHEMATICA
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Select[Range[10^5], IntegerQ[#1 (#1 - #2)/#3] & @@ Prepend[DivisorSigma[{0, 1}, #], #] &] (* Michael De Vlieger, Mar 24 2019 *)
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PROG
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(MAGMA) [n: n in [1..1000000] | IsIntegral((n - NumberOfDivisors(n)) * n / SumOfDivisors(n))]
(PARI) isok(m) = frac(m*(m-numdiv(m))/sigma(m)) == 0; \\ Michel Marcus, Mar 25 2019
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CROSSREFS
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Cf. A000005, A000203, A000396, A001599, A049820, A325021, A325022, A325023, A325024.
Sequence in context: A085286 A062085 A284632 * A335131 A147800 A246624
Adjacent sequences: A325017 A325018 A325019 * A325021 A325022 A325023
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KEYWORD
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nonn
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AUTHOR
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Jaroslav Krizek, Mar 24 2019
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STATUS
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approved
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