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A280098
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The sum of the divisors of 24*n - 1, divided by 24.
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5
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1, 2, 3, 5, 6, 7, 7, 8, 11, 10, 11, 14, 13, 17, 15, 16, 19, 18, 28, 20, 21, 24, 25, 31, 25, 30, 27, 31, 35, 30, 31, 35, 38, 41, 35, 36, 37, 38, 54, 46, 41, 45, 43, 53, 49, 46, 57, 48, 62, 55, 51, 55, 56, 76, 55, 60, 57, 63, 71, 60, 80, 62, 63, 77, 65, 66, 67
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OFFSET
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1,2
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COMMENTS
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Conjecture: only the integers k in {1, 3, 4, 6, 8, 12, 24} have the property that the sum of the divisors of (k*n-1)/k is always an integer. - Robert G. Wilson v, Dec 25 2016
The finite sequence mentioned in the above conjecture gives the sum of the divisors of the partition numbers of the first seven positive integers (cf. A139041). - Omar E. Pol, Dec 25 2016
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LINKS
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FORMULA
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24 * a(n) = sum of the divisors of A183010(n).
Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/18 = 0.548311... (A086463). - Amiram Eldar, Mar 28 2024
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EXAMPLE
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G.f. = x + 2*x^2 + 3*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 7*x^7 + 8*x^8 + 11*x^9 + ...
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MATHEMATICA
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a[ n_] := If[ n < 1, 0, DivisorSigma[ 1, 24 n - 1] / 24];
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PROG
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(PARI) {a(n) = if( n<1, 0, sigma(24*n - 1) / 24)};
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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