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%I #19 Jun 19 2019 08:43:47
%S 14,44,1334,1634,2295,2685,3195,17255,33998,42818,45716,79316,84134,
%T 122073,124676,125811,166934,239499,289454,294151,383594,440013,
%U 544334,605985,649154,655005,736515,1163624,1325511,1364104
%N Numbers k such that k and k+1 have the same sum of unitary divisors and the same number of divisors.
%H Amiram Eldar, <a href="/A064348/b064348.txt">Table of n, a(n) for n = 1..1204</a> (terms 1..75 from Harry J. Smith)
%t g[1]={1,1}; g[n_] := {Times @@ ((f = FactorInteger[n])[[;;,2]] + 1), Times @@ (1 + Power @@@ f)}; 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 (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); } for(n=1,10^6, if(usigma(n)==usigma(n+1) && numdiv(n)==numdiv(n+1),print1(n,",")))
%o (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) } { n=0; s=0; d=0; for (m=1, 10^9, us=usigma(m + 1); ud=numdiv(m + 1); if(s==us && d==ud, write("b064348.txt", n++, " ", m); if (n==100, break)); s=us; d=ud ) } \\ _Harry J. Smith_, Sep 12 2009
%Y Cf. A000005, A034448, A064125.
%K nonn
%O 1,1
%A _Jason Earls_, Oct 15 2001
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