cp's OEIS Frontend

A072815 Sum of proper divisors of 6n + 1.

%I A072815 #17 Feb 16 2025 08:32:46
%S A072815 0,1,1,1,6,1,1,1,8,17,1,1,1,1,23,21,1,1,1,29,12,1,27,1,35,1,1,1,14,73,
%T A072815 1,29,1,1,47,1,39,1,1,53,1,33,35,45,59,1,1,1,18,65,51,1,1,41,109,1,1,
%U A072815 57,1,77,20,1,1,1,191,41,1,45,1,89,1,69,1,1,95,53,1
%N A072815 Sum of proper divisors of 6n + 1.
%C A072815 The square root of t(n) < s(t(4n-1, 4n-2, 4n-3, 4n-4)) < s(t(4n)).
%H A072815 T. D. Noe, <a href="/A072815/b072815.txt">Table of n, a(n) for n = 0..1000</a>
%H A072815 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RestrictedDivisorFunction.html">Restricted Divisor Function</a>.
%F A072815 a(n) = s(t(n)), where t(n) = 6n + 1 and s(n) is the restricted divisor function.
%F A072815 From _Amiram Eldar_, Apr 12 2024: (Start)
%F A072815 a(n) = A363031(n) - A016921(n) = A001065(A016921(n)).
%F A072815 Sum_{k=1..n} a(k) ~ c * n^2, where c = P^2/3 - 3 = A145426 = 0.289868... . (End)
%e A072815 a(1) = s(t(1)) = 1 since t(1) = 7 and s(7) = 1 under the definition of the restricted divisor function.
%t A072815 Table[c=6n+1; DivisorSigma[1,c]-c, {n,0,80}] (* _Harvey P. Dale_, Nov 13 2013 *)
%o A072815 (PARI) a(n) = sigma(6*n + 1) - 6*n - 1; \\ _Amiram Eldar_, Apr 12 2024
%Y A072815 Cf. A001065, A016921, A145426, A363031.
%K A072815 nonn
%O A072815 0,5
%A A072815 Hisanobu Shinya (ilikemathematics(AT)hotmail.com), Jul 14 2002
%E A072815 Corrected by _Harvey P. Dale_, Nov 13 2013