cp's OEIS Frontend

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

%I A280098 #39 Mar 28 2024 09:03:11
%S A280098 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,
%T A280098 30,27,31,35,30,31,35,38,41,35,36,37,38,54,46,41,45,43,53,49,46,57,48,
%U A280098 62,55,51,55,56,76,55,60,57,63,71,60,80,62,63,77,65,66,67
%N A280098 The sum of the divisors of 24*n - 1, divided by 24.
%C A280098 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
%C A280098 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
%H A280098 Ivan Neretin, <a href="/A280098/b280098.txt">Table of n, a(n) for n = 1..10000</a>
%F A280098 24 * a(n) = sum of the divisors of A183010(n).
%F A280098 a(n) = A280097(n)/24. - _Omar E. Pol_, Dec 25 2016
%F A280098 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
%e A280098 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 + ...
%t A280098 a[ n_] := If[ n < 1, 0, DivisorSigma[ 1, 24 n - 1] / 24];
%t A280098 DivisorSigma[1,24*Range[70]-1]/24 (* _Harvey P. Dale_, Sep 25 2017 *)
%o A280098 (PARI) {a(n) = if( n<1, 0, sigma(24*n - 1) / 24)};
%Y A280098 Cf. A000203, A086463, A139041, A183010, A280097.
%K A280098 nonn,easy
%O A280098 1,2
%A A280098 _Michael Somos_, Dec 25 2016