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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1375 (terms 1..190 from Harry J. Smith)

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 *)

Prog

(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

Crossrefs

Cf. A034448, A048146, A064125.

Sequence in context: A241110 A055152 A171183 * A189304 A123178 A208318

Adjacent sequences: A064726 A064727 A064728 * A064730 A064731 A064732

Keyword

nonn

Author

Jason Earls, Oct 17 2001

Extensions

a(27)-a(32) from Harry J. Smith, Sep 24 2009

Status

approved