cp's OEIS Frontend

A285313 Number of pairs (a,b) such that a*b = n and d(a) = d(b) with d = A000005 and a <= b.

%I A285313 #12 Apr 18 2017 22:44:36
%S A285313 1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,1,1,
%T A285313 1,2,0,1,1,0,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,
%U A285313 1,0,0,0,0,1,0,0,1,0,0,1,1,1,0,1,1,1,1,0,0,1
%N A285313 Number of pairs (a,b) such that a*b = n and d(a) = d(b) with d = A000005 and a <= b.
%H A285313 G. C. Greubel, <a href="/A285313/b285313.txt">Table of n, a(n) for n = 1..1000</a>
%H A285313 Project Euler, <a href="https://projecteuler.net/problem=598">Problem 598: Split Divisibilities</a>
%F A285313 a(p) = 0; for prime p and for an odd power of a prime.
%F A285313 a(p^2k) = 1, for an even power of a prime.
%t A285313 a[n_]:=Sum[Boole[d<=(n/d) && DivisorSigma[0, d] == DivisorSigma[0, n/d]], {d, Divisors[n]}]; Table[a[n], {n, 100}] (* _Indranil Ghosh_, Apr 18 2017 *)
%o A285313 (PARI) a(n) = sumdiv(n, d, (d <= n/d) && (numdiv(d) == numdiv(n/d)));
%o A285313 (Python)
%o A285313 from sympy import divisors, divisor_count
%o A285313 def a(n): return sum([d<=(n/d) and divisor_count(d)==divisor_count(n/d) for d in divisors(n)]) # _Indranil Ghosh_, Apr 18 2017
%Y A285313 Cf. A000005, A277621 (for n!).
%K A285313 nonn
%O A285313 1,36
%A A285313 _Michel Marcus_, Apr 17 2017