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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1204 (terms 1..75 from Harry J. Smith)

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 *)

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); } 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

Crossrefs

Cf. A000005, A034448, A064125.

Sequence in context: A031130 A215199 A216258 * A206215 A328243 A369240

Adjacent sequences: A064345 A064346 A064347 * A064349 A064350 A064351

Keyword

nonn

Author

Jason Earls, Oct 15 2001

Status

approved