cp's OEIS Frontend

A110176 Least k such that sigma(n) = sigma(k) + sigma(n-k) for 0 or 0 if there is no such k, where sigma is the sum of divisors function.

%I A110176 #10 Feb 20 2023 12:26:29
%S A110176 0,0,1,0,0,0,0,2,4,2,0,0,0,0,5,0,0,0,0,2,7,0,0,0,0,0,0,0,0,6,0,4,11,0,
%T A110176 0,0,0,0,13,10,0,0,0,0,0,0,0,0,8,0,17,0,0,0,12,14,19,0,0,0,0,17,19,0,
%U A110176 0,0,0,0,14,14,0,0,0,0,25,0,0,0,0,0,0,0,0,0,38,0,22,22,0,18,0,30,31,19,0,12
%N A110176 Least k such that sigma(n) = sigma(k) + sigma(n-k) for 0<k<n, or 0 if there is no such k, where sigma is the sum of divisors function.
%C A110176 Sequence A110177 gives the number of solutions 0<k<n. Note that a(n)=0 for all primes except 3. It is also zero for the composite numbers in A110178.
%H A110176 Antti Karttunen, <a href="/A110176/b110176.txt">Table of n, a(n) for n = 1..16384</a>
%H A110176 Antti Karttunen, <a href="/A110176/a110176.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%t A110176 a[n_] := Select[Range[n-1], DivisorSigma[1, n]==DivisorSigma[1, n-# ]+DivisorSigma[1, # ]&]; Table[s=a[n]; If[Length[s]==0, 0, First[s]], {n, 150}]
%o A110176 (PARI) A110176(n) = { my(x=sigma(n)); for(k=1,n-1,if(x == (sigma(k)+sigma(n-k)), return(k))); (0); }; \\ _Antti Karttunen_, Feb 20 2023
%Y A110176 Cf. A066435 (least k such that sigma(n)+sigma(k)=sigma(n+k)), A110177.
%Y A110176 Cf. also A110173.
%K A110176 nonn
%O A110176 1,8
%A A110176 _T. D. Noe_, Jul 15 2005