A063071 - OEIS

A063071

Numbers k such that sigma(k)*omega(k) = sigma(k+1)*omega(k+1), where omega(k) is the number of distinct prime divisors of n (A001221).

%I #17 Jun 28 2018 02:49:07

%S 14,206,1334,1634,2685,14841,18873,19358,26872,33998,36566,42818,

%T 56564,84134,116937,122073,161001,162602,166934,174717,190773,193893,

%U 239499,245768,260096,289454,326884,383594,409695,422073,430137,438993,440013

%N Numbers k such that sigma(k)*omega(k) = sigma(k+1)*omega(k+1), where omega(k) is the number of distinct prime divisors of n (A001221).

%H Giovanni Resta, <a href="/A063071/b063071.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Harry J. Smith)

%t Select[Range[5000], PrimeNu[#]*DivisorSigma[1, #] == PrimeNu[# + 1]*DivisorSigma[1, # + 1] &] (* _G. C. Greubel_, Apr 23 2017 *)

%o (PARI) for(n=1,10^6, if(sigma(n)*omega(n)==sigma(n+1)*omega(n+1),print(n)))

%o (PARI) { n=0; s=1; for (m=1, 10^9, if(s!=(r=sigma(m)*omega(m)), s=r, write("b063071.txt", n++, " ", m - 1); if (n==100, break)) ) } \\ _Harry J. Smith_, Aug 16 2009

%Y Cf. A001221, A002961, A000203.

%K easy,nonn

%O 1,1

%A _Jason Earls_, Aug 04 2001