A280098 The sum of the divisors of 24*n - 1, divided by 24.

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

Offset

1,2

Comments

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

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

24 * a(n) = sum of the divisors of A183010(n).

a(n) = A280097(n)/24. - Omar E. Pol, Dec 25 2016

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

Example

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 + ...

Mathematica

a[ n_] := If[ n < 1, 0, DivisorSigma[ 1, 24 n - 1] / 24];
DivisorSigma[1, 24*Range[70]-1]/24 (* Harvey P. Dale, Sep 25 2017 *)

Prog

(PARI) {a(n) = if( n<1, 0, sigma(24*n - 1) / 24)};

Crossrefs

Cf. A000203, A086463, A139041, A183010, A280097.

Sequence in context: A113821 A319523 A255367 * A019517 A031976 A023839

Adjacent sequences: A280095 A280096 A280097 * A280099 A280100 A280101

Keyword

nonn,easy

Author

Michael Somos, Dec 25 2016

Status

approved