A064729 Numbers k such that k and k+1 have the same sum of unitary and nonunitary divisors.
14, 957, 1334, 1634, 2685, 20145, 33998, 42818, 74918, 79826, 79833, 84134, 111506, 122073, 138237, 147454, 166934, 201597, 274533, 289454, 347738, 383594, 416577, 440013, 544334, 605985, 649154, 655005, 1642154, 1857513, 2168906, 2284814
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1375 (terms 1..190 from Harry J. Smith)
Programs
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Mathematica
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 *) -
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,","))) -
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
Extensions
a(27)-a(32) from Harry J. Smith, Sep 24 2009