login
Numbers k for which d(k+1) > 2d(k), where d(j) = A000005(j).
1

%I #14 Nov 16 2020 15:04:38

%S 11,17,19,23,29,31,35,41,43,47,53,59,67,71,79,83,89,95,97,101,103,107,

%T 109,111,113,119,125,127,131,137,139,143,149,151,155,159,161,163,167,

%U 169,173,179,181,191,197,199,203,209,211,215,219,223,227,229,233,239

%N Numbers k for which d(k+1) > 2d(k), where d(j) = A000005(j).

%C d(p+1) >= 2d(p) holds for all primes p and for some integers, as well.

%H Harry J. Smith, <a href="/A063449/b063449.txt">Table of n, a(n) for n = 1..1000</a>

%e n=29: 2d(29) = 2*2 = 4 < 8 = d(30);

%e n=95: 2d(95) = 2*4 = 8 < 12 = d(96).

%t Position[Partition[DivisorSigma[0,Range[250]],2,1],_?(2#[[1]]<#[[2]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Nov 16 2020 *)

%o (PARI) { n=0; for (m=1, 10^9, if (numdiv(m + 1) > 2*numdiv(m), write("b063449.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 21 2009

%Y Cf. A000005.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 24 2001

%E Edited by _Jon E. Schoenfield_, Sep 05 2017