A064348 Numbers k such that k and k+1 have the same sum of unitary divisors and the same number of divisors.
14, 44, 1334, 1634, 2295, 2685, 3195, 17255, 33998, 42818, 45716, 79316, 84134, 122073, 124676, 125811, 166934, 239499, 289454, 294151, 383594, 440013, 544334, 605985, 649154, 655005, 736515, 1163624, 1325511, 1364104
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1204 (terms 1..75 from Harry J. Smith)
Programs
-
Mathematica
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 *) -
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,","))) -
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