A121615 - OEIS

%I #6 Apr 04 2015 21:38:08

%S 2,3,5,7,11,13,15,17,19,23,29,31,35,37,41,43,47,49,53,59,61,67,71,73,

%T 79,83,89,97,101,103,107,109,113,121,127,131,137,139,143,149,151,157,

%U 163,167,169,173,179,181,187,191,193,197,199,211,221,223,227,229,233,239

%N Lexicographically earliest sequence such that the k-th prime occurs altogether not more than k times as prime factor.

%C Subsequence of A037143: 1 <= A001222(a(n)) <= 2; A000040 is a subsequence.

%H R. Zumkeller, <a href="/A121615/b121615.txt">Table of n, a(n) for n = 1..1000</a>

%e k=1, prime(1)=2: {2} = {a(1)},

%e k=2, prime(2)=3: {3,3*5} = {a(2),a(7)},

%e k=3, prime(3)=5: {5,3*5,5*7} = {a(3),a(7),a(13)},

%e k=4, prime(4)=7: {7,5*7,7*7} = {a(4),a(7),a(18)},

%e k=5, prime(5)=11: {11,11*11,11*13,11*17} = {a(5),a(34),a(39),a(49)},

%e k=6, prime(6)=13: {13,11*13,13*13,13*17,13*19} = {a(6),a(39),a(45),a(55),a(62)};

%e k=7, prime(7)=17: {17,11*17,13*17,17*17,17*19,17*23} = {a(8),a(49),a(55),a(71),a(77),a(90)}.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Aug 11 2006