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A263025 n is the a(n)-th positive integer having its sum of divisors.

%I A263025 #26 Oct 09 2015 18:03:23
%S A263025 1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,1,1,3,1,2,2,1,1,1,1,2,1,1,1,
%T A263025 2,1,1,2,2,1,3,1,1,1,1,2,3,1,1,1,3,1,2,1,4,2,1,2,3,1,1,2,1,1,2,1,1,1,
%U A263025 3,2,5,1,1,1,2,1,4,2,2,1,1,2,3,1,1,1,3
%N A263025 n is the a(n)-th positive integer having its sum of divisors.
%C A263025 Sum of divisors is given by A000203.
%C A263025 This can also be described as the ordinal transform of A000203. - _Franklin T. Adams-Watters_, Oct 09 2015
%C A263025 a(n) > 1 iff n is in A069822.
%H A263025 Paul Tek, <a href="/A263025/b263025.txt">Table of n, a(n) for n = 1..25000</a>
%F A263025 a(A034885(k))=1 for k>0.
%e A263025 The numbers with sum of divisors 72 are: 30, 46, 51, 55, 71.
%e A263025 Hence: a(30)=1, a(46)=2, a(51)=3, a(55)=4, a(71)=5.
%e A263025 More generally: the terms of each row of A085790 (say of length i) map to 1, 2, ..., i.
%e A263025 Also: for any n>0, the n terms of the n-th row of A201915 map to 1, 2, ..., n.
%p A263025 N:= 1000: # to get a(1) to a(N)
%p A263025 Sigmas:= [seq(numtheory:-sigma(i),i=1..N)]:
%p A263025 seq(numboccur(Sigmas[n], Sigmas[1..n]),n=1..N); # _Robert Israel_, Oct 09 2015
%t A263025 t = DivisorSigma[1, #] & /@ Range@ 10000; s = Position[t, #] & /@ Range@ Max@ t; Flatten[Position[s, #, {3}]][[2]] & /@ Range@ 87 (* _Michael De Vlieger_, Oct 09 2015 *)
%o A263025 (PARI) cnt = vector(224); for (n=1, 87, s=sigma(n); cnt[s] = cnt[s]+1; print1(cnt[s] ", "))
%Y A263025 Cf. A000203, A034885, A069822, A078898, A085790, A201915.
%K A263025 nonn,look
%O A263025 1,11
%A A263025 _Paul Tek_, Oct 09 2015