This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335182 #51 Jul 09 2025 04:53:18
%S A335182 1,3,1,3,1,3,1,11,10,3,1,15,1,3,1,11,1,30,1,3,1,3,1,47,1,3,10,3,1,3,1,
%T A335182 11,1,3,1,78,1,3,1,51,1,3,1,3,10,3,1,47,1,3,1,3,1,30,1,67,1,3,1,75,1,
%U A335182 3,10,11,1,3,1,3,1,3,1,182,1,3,1,3,1,3,1,131,10,3,1,99
%N A335182 Sum of the refactorable divisors of n.
%C A335182 Inverse Möbius transform of n * c(n), where c(n) is the characteristic function of refactorable numbers (A336040). - _Wesley Ivan Hurt_, Jun 21 2024
%H A335182 Antti Karttunen, <a href="/A335182/b335182.txt">Table of n, a(n) for n = 1..20000</a>
%H A335182 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RefactorableNumber.html">Refactorable Number</a>
%F A335182 a(n) = Sum_{d|n} d * c(d), where c = A336040.
%F A335182 a(n) = Sum_{d|n} d * (1 - ceiling(d/tau(d)) + floor(d/tau(d))), where tau(n) is the number of divisors of n (A000005).
%F A335182 a(n) = A349322(n) - A349658(n). - _Antti Karttunen_, Nov 24 2021
%F A335182 a(p) = 1 for odd primes p. - _Wesley Ivan Hurt_, Nov 28 2021
%e A335182 a(6) = 3; The divisors of 6 are {1,2,3,6}. 1 and 2 are refactorable since d(1) = 1|1 and d(2) = 2|2, so a(6) = 1 + 2 = 3.
%e A335182 a(7) = 1; The divisors of 7 are {1,7} and 1 is the only refactorable divisor of 7. So a(7) = 1.
%e A335182 a(8) = 11; The divisors of 8 are {1,2,4,8}. 1, 2 and 8 are refactorable since d(1) = 1|1, d(2) = 2|2 and d(8) = 4|8, so a(8) = 1 + 2 + 8 = 11.
%e A335182 a(9) = 10; The divisors of 9 are {1,3,9}. 1 and 9 are refactorable since d(1) = 1|1 and d(9) = 3|9, so a(9) = 1 + 9 = 10.
%t A335182 a[n_] := DivisorSum[n, # &, Divisible[#, DivisorSigma[0, #]] &]; Array[a, 80] (* _Amiram Eldar_, Nov 24 2021 *)
%o A335182 (PARI) isr(n) = n%numdiv(n)==0; \\ A033950
%o A335182 a(n) = sumdiv(n, d, if (isr(d), d)); \\ _Michel Marcus_, Jul 20 2020
%Y A335182 Cf. A000005 (tau), A033950 (refactorable numbers), A336040 (refactorable characteristic), A336041 (number of refactorable divisors), A335665 (their product).
%Y A335182 Difference of A349322 and A349658.
%K A335182 nonn,easy
%O A335182 1,2
%A A335182 _Wesley Ivan Hurt_, Jul 17 2020