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 A322966 #29 Feb 19 2019 02:43:50 %S A322966 1,2,3,1,5,1,7,2,3,5,11,3,13,7,5,1,17,2,19,5,21,11,23,3,5,13,1,7,29,5, %T A322966 31,2,11,17,35,3,37,19,39,1,41,7,43,11,1,23,47,1,7,10,17,13,53,1,55,7, %U A322966 57,29,59,5,61,31,21,1,65,11,67,17,23,35,71,6,73,37,15,19,77,13,79,5 %N A322966 Denominator of Sum_{d | n} 1/rad(d) where rad = A007947. %C A322966 Let rad(n) be the radical of n, which equals the product of all prime factors of n (A007947). Let f(n) = Sum_{d | n} 1/rad(n). The sequence a(n) lists the denominators of the fractions f(n) in lowest terms. %C A322966 f is a multiplicative function whose value on a prime power is f(p^k) = 1 + k/p. Hence f is a weighted divisor-counting function that weights divisors d higher when they have few and small prime divisors themselves. %e A322966 The divisors of 12 are 1,2,3,4,6,12, so f(12) = 1 + (1/2) + (1/3) + (1/2) + (1/6) + (1/6) = 8/3, and a(12) = 3. Alternately, since f is multiplicative, f(12) = f(4)*f(3) = (1+2/2)*(1+1/3) = 8/3. The denominator of f(12) is 3 hence a(12) = 3. %t A322966 Array[Denominator@ DivisorSum[#, 1/Apply[Times, FactorInteger[#][[All, 1]] ] &] &, 80] (* _Michael De Vlieger_, Jan 19 2019 *) %o A322966 (PARI) a(n) = denominator(sumdiv(n, d, 1/factorback(factor(d)[, 1]))) \\ _David A. Corneth_, Jan 01 2019 %Y A322966 Cf. A007947 (radical), A322965 (numerators). %Y A322966 Numbers n where f(n) increases to a record: A322447. %K A322966 frac,nonn %O A322966 1,2 %A A322966 _David S. Metzler_, Dec 31 2018