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A137179 a(n) = the smallest positive integer m such that d(m) + d(m+1) = n, where d(m) is the number of positive divisors of m. (a(n) is the smallest m where A092405(m) = n.)

%I A137179 #11 Mar 31 2021 19:21:14
%S A137179 1,2,3,5,8,11,15,20,24,39,35,59,80,84,195,167,120,119,224,239,399,335,
%T A137179 440,359,360,480,1520,539,899,719,1224,720,840,1079,3135,1259,5183,
%U A137179 1260,2400,2160,1680,1679,9408,2880,7056,2639,3024,2520,6240,2519,7055,6929
%N A137179 a(n) = the smallest positive integer m such that d(m) + d(m+1) = n, where d(m) is the number of positive divisors of m. (a(n) is the smallest m where A092405(m) = n.)
%H A137179 Robert Israel, <a href="/A137179/b137179.txt">Table of n, a(n) for n = 3..250</a>
%p A137179 N:= 100: # for a(3)..a(N)
%p A137179 V:= Array(3..N):
%p A137179 count:= 0: dp:= 1:
%p A137179 for m from 1 while count < N-2 do
%p A137179   d:= dp; dp:= numtheory:-tau(m+1);
%p A137179   v:= d+dp;
%p A137179   if v <= N and V[v] = 0 then
%p A137179     V[v]:= m;
%p A137179     count:= count+1;
%p A137179   fi
%p A137179 od:
%p A137179 convert(V,list); # _Robert Israel_, Mar 31 2021
%t A137179 a = {}; For[n = 3, n < 60, n++, i = 1; While[ ! DivisorSigma[0, i] + DivisorSigma[0, i + 1] == n, i++ ]; AppendTo[a, i]]; a (* _Stefan Steinerberger_, May 18 2008 *)
%Y A137179 Cf. A092405.
%K A137179 nonn
%O A137179 3,2
%A A137179 _Leroy Quet_, May 11 2008
%E A137179 More terms from _Stefan Steinerberger_, May 18 2008