A072815 - OEIS

%I #16 Apr 12 2024 03:29:57

%S 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 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 57,1,77,20,1,1,1,191,41,1,45,1,89,1,69,1,1,95,53,1

%N Sum of proper divisors of 6n + 1.

%C The square root of t(n) < s(t(4n-1, 4n-2, 4n-3, 4n-4)) < s(t(4n)).

%H T. D. Noe, <a href="/A072815/b072815.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RestrictedDivisorFunction.html">Restricted Divisor Function</a>.

%F a(n) = s(t(n)), where t(n) = 6n + 1 and s(n) is the restricted divisor function.

%F From _Amiram Eldar_, Apr 12 2024: (Start)

%F a(n) = A363031(n) - A016921(n) = A001065(A016921(n)).

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = P^2/3 - 3 = A145426 = 0.289868... . (End)

%e a(1) = s(t(1)) = 1 since t(1) = 7 and s(7) = 1 under the definition of the restricted divisor function.

%t Table[c=6n+1; DivisorSigma[1,c]-c, {n,0,80}] (* _Harvey P. Dale_, Nov 13 2013 *)

%o (PARI) a(n) = sigma(6*n + 1) - 6*n - 1; \\ _Amiram Eldar_, Apr 12 2024

%Y Cf. A001065, A016921, A145426, A363031.

%K nonn

%O 0,5

%A Hisanobu Shinya (ilikemathematics(AT)hotmail.com), Jul 14 2002

%E Corrected by _Harvey P. Dale_, Nov 13 2013