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 A285313 Number of pairs (a,b) such that a*b = n and d(a) = d(b) with d = A000005 and a <= b. 1
 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, 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, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,36 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Project Euler, Problem 598: Split Divisibilities FORMULA a(p) = 0; for prime p and for an odd power of a prime. a(p^2k) = 1, for an even power of a prime. MATHEMATICA 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 *) PROG (PARI) a(n) = sumdiv(n, d, (d <= n/d) && (numdiv(d) == numdiv(n/d))); (Python) from sympy import divisors, divisor_count 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 CROSSREFS Cf. A000005, A277621 (for n!). Sequence in context: A154469 A344584 A037273 * A231366 A158924 A025426 Adjacent sequences:  A285310 A285311 A285312 * A285314 A285315 A285316 KEYWORD nonn AUTHOR Michel Marcus, Apr 17 2017 STATUS approved

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Last modified September 17 16:00 EDT 2021. Contains 347478 sequences. (Running on oeis4.)