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 A124315 #60 Oct 22 2022 08:06:12
%S A124315 1,2,2,4,2,4,2,6,4,4,2,8,2,4,4,9,2,8,2,8,4,4,2,12,4,4,6,8,2,8,2,12,4,
%T A124315 4,4,16,2,4,4,12,2,8,2,8,8,4,2,18,4,8,4,8,2,12,4,12,4,4,2,16,2,4,8,16,
%U A124315 4,8,2,8,4,8,2,24,2,4,8,8,4,8,2,18,9,4,2,16,4,4,4,12,2,16,4,8,4,4,4,24,2,8
%N A124315 a(n) = Sum_{ d divides n } tau(gcd(d,n/d)), where tau = sigma_0 = A000005.
%C A124315 Apparently the Mobius transform of A046951. - _R. J. Mathar_, Feb 07 2011
%C A124315 Number of ordered pairs of divisors of n, (d1,d2), with d1<=d2, such that d1|d2 and n|(d1*d2). - _Wesley Ivan Hurt_, Mar 22 2022
%H A124315 Antti Karttunen, <a href="/A124315/b124315.txt">Table of n, a(n) for n = 1..10000</a>
%H A124315 László Tóth, <a href="http://arxiv.org/abs/1310.7053">Multiplicative arithmetic functions of several variables: a survey</a>, arXiv preprint arXiv:1310.7053 [math.NT], 2013-2014.
%F A124315 a(p) = 2 iff p is a prime.
%F A124315 Multiplicative with a(p^e) = e+1+floor(e^2/4). - _R. J. Mathar_, Apr 14 2011
%F A124315 Dirichlet g.f.: zeta(s)^2 * zeta(2*s). - _Vaclav Kotesovec_, Jan 11 2019
%F A124315 Sum_{k=1..n} a(k) ~ (Pi^2/6) * (n*log(n) + (2*gamma - 1 + 2*zeta'(2)/zeta(2))*n), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Oct 22 2022
%p A124315 A124315 := proc(n) local a,d; a := 0 ; for d in numtheory[divisors](n) do igcd(d,n/d) ; a := a+numtheory[tau](%) ; end do: a; end proc: # _R. J. Mathar_, Apr 14 2011
%t A124315 Table[Plus @@ Map[DivisorSigma[0, GCD[ #, n/# ]] &, Divisors@n], {n, 98}]
%t A124315 f[p_, e_] := e + 1 + Floor[e^2/4]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Apr 10 2022 *)
%o A124315 (PARI) a(n) = sumdiv(n, d, numdiv(gcd(d, n/d))); \\ _Michel Marcus_, Feb 12 2016
%o A124315 (Python)
%o A124315 from sympy import divisors, divisor_count, gcd
%o A124315 def a(n): return sum([divisor_count(gcd(d, n/d)) for d in divisors(n)]) # _Indranil Ghosh_, May 25 2017
%Y A124315 Cf. A000005, A001616, A001620, A046951, A061884, A124316, A306016.
%K A124315 mult,nonn
%O A124315 1,2
%A A124315 _Robert G. Wilson v_, Sep 30 2006