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 A064348 Numbers k such that k and k+1 have the same sum of unitary divisors and the same number of divisors. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 23 11:57 EDT 2024. Contains 372763 sequences. (Running on oeis4.)