Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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