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

Author

Michael Somos, Dec 25 2016

Keywords

• nonn
• easy

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

Examples

			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 + ...
		

Links

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

Crossrefs

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

Programs

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 *)

PARI

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

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