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 A206787 #63 Oct 10 2024 15:16:58
%S A206787 1,1,4,1,6,4,8,1,4,6,12,4,14,8,24,1,18,4,20,6,32,12,24,4,6,14,4,8,30,
%T A206787 24,32,1,48,18,48,4,38,20,56,6,42,32,44,12,24,24,48,4,8,6,72,14,54,4,
%U A206787 72,8,80,30,60,24,62,32,32,1,84,48,68,18,96,48,72,4
%N A206787 Sum of the odd squarefree divisors of n.
%C A206787 a(A000079(n)) = 1; a(A057716(n)) > 1; a(A065119(n)) = 4; a(A086761(n)) = 6.
%C A206787 Inverse Mobius transform of 1, 0, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 15, 0, 17, 0, 19, 0, 21, 0, 23, 0, 0, 0, 0, 0, 29... - _R. J. Mathar_, Jul 12 2012
%H A206787 Reinhard Zumkeller, <a href="/A206787/b206787.txt">Table of n, a(n) for n = 1..10000</a>
%H A206787 Jon Maiga, <a href="http://sequencedb.net/s/A206787">Computer-generated formulas for A206787</a>, Sequence Machine.
%F A206787 a(n) = Sum_{k = 1..A034444(n)} (A206778(n,k) mod 2) * A206778(n,k).
%F A206787 a(n) = Sum_{d|n} d*mu(2*d)^2, where mu is the Möbius function (A008683). - _Ridouane Oudra_, Aug 14 2019
%F A206787 Multiplicative with a(2^e) = 1, and a(p^e) = p + 1 for p > 2. - _Amiram Eldar_, Sep 18 2020
%F A206787 Sum_{k=1..n} a(k) ~ (1/3) * n^2. - _Amiram Eldar_, Nov 17 2022
%F A206787 Dirichlet g.f.: (zeta(s)*zeta(s-1)/zeta(2*s-2))*(2^s/(2^s+2)). - _Amiram Eldar_, Jan 03 2023
%F A206787 From _Antti Karttunen_, Nov 22 2023: (Start)
%F A206787 a(n) = A000203(A204455(n)) = A000593(A007947(n)) = A048250(n)/A010684(n-1). [From Sequence Machine]
%F A206787 a(n) = Sum_{d|n} abs(A349343(d)). [See _R. J. Mathar_'s Jul 12 2012 comment above]
%F A206787 (End)
%F A206787 a(n) = Sum_{d divides n, d odd} d * mu(d)^2. - _Peter Bala_, Feb 01 2024
%p A206787 seq(add(d*mobius(2*d)^2, d in divisors(n)), n=1 .. 80); # _Ridouane Oudra_, Aug 14 2019
%t A206787 a[n_] := DivisorSum[n, #*Boole[OddQ[#] && SquareFreeQ[#]]&]; Array[a, 80] (* _Jean-François Alcover_, Dec 05 2015 *)
%t A206787 f[2, e_] := 1; f[p_, e_] := p + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 18 2020 *)
%o A206787 (Haskell)
%o A206787 a206787 = sum . filter odd . a206778_row
%o A206787 (PARI) a(n) = sumdiv(n, d, d*(d % 2)*issquarefree(d)); \\ _Michel Marcus_, Sep 21 2014
%o A206787 (Magma) [&+[d:d in Divisors(m)|IsOdd(d) and IsSquarefree(d)]:m in [1..72]]; // _Marius A. Burtea_, Aug 14 2019
%o A206787 (Python)
%o A206787 from math import prod
%o A206787 from sympy import primefactors
%o A206787 def A206787(n): return prod(1+(p if p>2 else 0) for p in primefactors(n)) # _Chai Wah Wu_, Oct 10 2024
%Y A206787 Cf. A000203, A000593, A007947, A008683, A056911, A048250, A010684, A192066, A204455.
%Y A206787 Cf. A000079, A057716, A065119, A086761.
%Y A206787 Inverse Möbius transform of the absolute values of A349343.
%K A206787 nonn,mult,easy
%O A206787 1,3
%A A206787 _Reinhard Zumkeller_, Feb 12 2012