A285313 - OEIS

%I #12 Apr 18 2017 22:44:36

%S 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 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 1,0,0,0,0,1,0,0,1,0,0,1,1,1,0,1,1,1,1,0,0,1

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

%H G. C. Greubel, <a href="/A285313/b285313.txt">Table of n, a(n) for n = 1..1000</a>

%H Project Euler, <a href="https://projecteuler.net/problem=598">Problem 598: Split Divisibilities</a>

%F a(p) = 0; for prime p and for an odd power of a prime.

%F a(p^2k) = 1, for an even power of a prime.

%t 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 (PARI) a(n) = sumdiv(n, d, (d <= n/d) && (numdiv(d) == numdiv(n/d)));

%o (Python)

%o from sympy import divisors, divisor_count

%o 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 Cf. A000005, A277621 (for n!).

%K nonn

%O 1,36

%A _Michel Marcus_, Apr 17 2017