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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.)
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%I #11 Mar 31 2021 19:21:14

%S 1,2,3,5,8,11,15,20,24,39,35,59,80,84,195,167,120,119,224,239,399,335,

%T 440,359,360,480,1520,539,899,719,1224,720,840,1079,3135,1259,5183,

%U 1260,2400,2160,1680,1679,9408,2880,7056,2639,3024,2520,6240,2519,7055,6929

%N 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 Robert Israel, <a href="/A137179/b137179.txt">Table of n, a(n) for n = 3..250</a>

%p N:= 100: # for a(3)..a(N)

%p V:= Array(3..N):

%p count:= 0: dp:= 1:

%p for m from 1 while count < N-2 do

%p d:= dp; dp:= numtheory:-tau(m+1);

%p v:= d+dp;

%p if v <= N and V[v] = 0 then

%p V[v]:= m;

%p count:= count+1;

%p fi

%p od:

%p convert(V,list); # _Robert Israel_, Mar 31 2021

%t 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 Cf. A092405.

%K nonn

%O 3,2

%A _Leroy Quet_, May 11 2008

%E More terms from _Stefan Steinerberger_, May 18 2008