This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A275693 #5 Aug 12 2016 22:49:07 %S A275693 1,2,4,6,7,30,210,211,212,213,214,215,216,217,218,219,220,221,222,223, %T A275693 224,225,226,227,228,229,230,231,232,2310,2311,2312,2313,2314,2315, %U A275693 2316,2317,2318,2319,2320,2321,2322,2323,2324,2325,2326,2327,2328,2329,2330 %N A275693 Lexicographically earliest increasing sequence such that the a(n)th term of the sequence has n noncomposite divisors. %C A275693 We let tau_nc(n) = number of noncomposite divisors of n = A083399(n) = A001221(n) + 1 = omega(n) + 1. %C A275693 Primorial numbers from A002110 are terms. %H A275693 Jaroslav Krizek, <a href="/A275693/b275693.txt">Table of n, a(n) for n = 1..250</a> %F A275693 tau_nc(a(a(n))) = A083399(a(a(n))) = A001221(a(a(n))) + 1 = omega(a(a(n))) + 1 = n. %e A275693 a(1)=1 because tau_nc(1)=1; a(2)=2 because tau_nc(2)=2; a(3) cannot be 3 because tau_nc(3)=2, a(3)=4 (4 is the smallest number x>3); if a(3)=4, a(4) must be the smallest number x>a(3) with 3 noncomposite divisors, a(4)=6; a(6) must be number with 4 noncomposite divisors and must keep increase of the sequence, a(6)=30; a(5)=7 because 7>a(4); a(7) must be the smallest number with 5 noncomposite divisors because a(5)=7, a(7)=210; if a(6)=30, a(30) must be the smallest number x>a(7) with 6 noncomposite divisors and must keep increase of the sequence, a(30)=2310; a(8)-a(29) are numbers from interval 211-232; etc... %Y A275693 Cf. A001221, A002110, A083399, A275658. %K A275693 nonn %O A275693 1,2 %A A275693 _Jaroslav Krizek_, Aug 05 2016