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A064729 Numbers k such that k and k+1 have the same sum of unitary and nonunitary divisors.

%I A064729 #19 Jun 19 2019 08:16:40
%S A064729 14,957,1334,1634,2685,20145,33998,42818,74918,79826,79833,84134,
%T A064729 111506,122073,138237,147454,166934,201597,274533,289454,347738,
%U A064729 383594,416577,440013,544334,605985,649154,655005,1642154,1857513,2168906,2284814
%N A064729 Numbers k such that k and k+1 have the same sum of unitary and nonunitary divisors.
%H A064729 Amiram Eldar, <a href="/A064729/b064729.txt">Table of n, a(n) for n = 1..1375</a> (terms 1..190 from Harry J. Smith)
%t A064729 g[1]={1, 1}; g[n_] := { Times @@ (1 + Power @@@ (f = FactorInteger[n])), Times @@ ((f[[;; , 1]]^(f[[;;,2]]+1)- 1)/(f[[;;,1]]-1))}; s={}; g1={0, 0}; Do[g2=g[n]; If[g1==g2, AppendTo[s, n-1]]; g1=g2, {n, 1, 50000}]; s (* _Amiram Eldar_, Jun 19 2019 *)
%o A064729 (PARI) {usigma(n, s=1, fac, i) = fac=factor(n); for(i=1,matsize(fac)[1],s=s*(1+fac[i,1]^fac[i,2])); return(s); } nu(n) = sigma(n)-usigma(n); for(n=1,10^7, if(usigma(n)==usigma(n+1) && nu(n)==nu(n+1), print1(n,",")))
%o A064729 (PARI) usigma(n)= { local(f,s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) } nu(n)= { sigma(n) - usigma(n) } { n=0; for (m = 1, 10^10, if(usigma(m)==usigma(m + 1) && nu(m)==nu(m + 1), write("b064729.txt", n++, " ", m); if (n==190, break)) ) } \\ _Harry J. Smith_, Sep 24 2009
%Y A064729 Cf. A034448, A048146, A064125.
%K A064729 nonn
%O A064729 1,1
%A A064729 _Jason Earls_, Oct 17 2001
%E A064729 a(27)-a(32) from _Harry J. Smith_, Sep 24 2009