cp's OEIS Frontend

A234367 Numbers such that gcd(sigma(n), n) != 1 and numerator(sigma(n)/n) > n.

%I A234367 #47 Jan 29 2025 12:55:52
%S A234367 20,70,80,104,160,208,272,320,350,416,464,490,544,550,650,770,832,928,
%T A234367 1088,1184,1190,1280,1300,1312,1332,1430,1610,1664,1696,1700,1750,
%U A234367 1856,1870,1952,2170,2196,2210,2368,2420,2530,2560,2590,2624,2628,2750,2990,3010
%N A234367 Numbers such that gcd(sigma(n), n) != 1 and numerator(sigma(n)/n) > n.
%C A234367 For numbers in A014567, we have A017665(n) = numerator(sigma(n)/n) = sigma(n) = A000203(n), so A017665(n) > n.
%C A234367 For numbers in A069059, since both terms of the fraction are divisible by their GCD, A009194(n), we will have A017665(n) < A000203(n).
%C A234367 Here we are interested in terms of A069059 for which we still have A017665(n) > n, despite the division by the GCD.
%C A234367 Numbers such that sigma(n)/n > gcd(sigma(n), n) > 1. - _Charlie Neder_, Sep 08 2018
%H A234367 Robert G. Wilson v, <a href="/A234367/b234367.txt">Table of n, a(n) for n = 1..10519</a> (First 6892 terms from Charlie Neder).
%e A234367 For n=20, we have A000203(20) = sigma(20) = 42, and since gcd(42, 20) != 1, then A017665(20) = numerator(42/20) = numerator(21/10) = 21 < sigma(20), but still A017665(20) > 20.
%t A234367 gnQ[n_]:=Module[{s=DivisorSigma[1,n]},GCD[s,n]!=1&&Numerator[s/n]>n]; Select[ Range[ 3100],gnQ] (* _Harvey P. Dale_, Jan 03 2018 *)
%o A234367 (PARI) isok(n) = (gcd(sigma(n), n) != 1) && (numerator(sigma(n)/n) > n);
%Y A234367 Cf. A000203, A009194, A014567, A017665, A069059.
%K A234367 nonn,nice
%O A234367 1,1
%A A234367 _Michel Marcus_, Dec 28 2013