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 A064729 Numbers k such that k and k+1 have the same sum of unitary and nonunitary divisors. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 23 19:48 EDT 2021. Contains 347617 sequences. (Running on oeis4.)