cp's OEIS Frontend

A229945 Triangle read by rows in which row n lists the union of the primes <= n and the divisors of n.

%I A229945 #21 Dec 02 2013 16:10:42
%S A229945 1,1,2,1,2,3,1,2,3,4,1,2,3,5,1,2,3,5,6,1,2,3,5,7,1,2,3,4,5,7,8,1,2,3,
%T A229945 5,7,9,1,2,3,5,7,10,1,2,3,5,7,11,1,2,3,4,5,6,7,11,12,1,2,3,5,7,11,13,
%U A229945 1,2,3,5,7,11,13,14,1,2,3,5,7,11,13,15,1,2,3,4,5,7,8,11,13,16
%N A229945 Triangle read by rows in which row n lists the union of the primes <= n and the divisors of n.
%C A229945 Also row n lists the divisors of n and the primes < n that do not divide n, in increasing order.
%C A229945 Also row n lists the nonprime divisors of n and the primes <= n, in increasing order.
%C A229945 Note that if n is 1 or prime then row n lists the first A036234(n) terms of A008578.
%C A229945 The motivation for this sequence is A046022 which is also the union of the odd primes and the divisors of 4. Here the n-th row of triangle can be interpreted as the initial terms of the infinite sequence defined as the union of the prime numbers and the divisors of n.
%e A229945 For n = 10, the divisors of 10 are 1, 2, 5, 10. The primes less than 10 that do not divide 10 are 3 and 7. So row 10 is 1, 2, 3, 5, 7, 10.
%e A229945 On the other hand, the primes <= n are 2, 3, 5, 7. The nonprime divisors of n are 1, 10. So row 10 is 1, 2, 3, 5, 7, 10.
%e A229945 Written as an irregular triangle the sequence begins:
%e A229945 1;
%e A229945 1, 2;
%e A229945 1, 2, 3;
%e A229945 1, 2, 3, 4;
%e A229945 1, 2, 3, 5;
%e A229945 1, 2, 3, 5, 6;
%e A229945 1, 2, 3, 5, 7;
%e A229945 1, 2, 3, 4, 5, 7, 8;
%e A229945 1, 2, 3, 5, 7, 9;
%e A229945 1, 2, 3, 5, 7, 10;
%e A229945 1, 2, 3, 5, 7, 11;
%e A229945 1, 2, 3, 4, 5, 6, 7, 11, 12;
%e A229945 1, 2, 3, 5, 7, 11, 13;
%e A229945 1, 2, 3, 5, 7, 11, 13, 14;
%e A229945 1, 2, 3, 5, 7, 11, 13, 15;
%e A229945 1, 2, 3, 4, 5, 7, 8, 11, 13, 16;
%e A229945 1, 2, 3, 5, 7, 11, 13, 17;
%e A229945 1, 2, 3, 5, 6, 7, 9, 11, 13, 17, 18;
%e A229945 1, 2, 3, 5, 7, 11, 13, 17, 19;
%e A229945 1, 2, 3, 4, 5, 7, 10, 11, 13, 17, 19, 20;
%e A229945 1, 2, 3, 5, 7, 11, 13, 17, 19, 21;
%e A229945 1, 2, 3, 5, 7, 11, 13, 17, 19, 22;
%e A229945 1, 2, 3, 5, 7, 11, 13, 17, 19, 23;
%e A229945 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 17, 19, 23, 24;
%Y A229945 Columns 1-3: A000012, A007395, A010701.
%Y A229945 Right border gives A000027.
%Y A229945 Cf. A000005, A000040, A000720, A008578, A027750, A036234, A046022.
%K A229945 nonn,tabf,less
%O A229945 1,3
%A A229945 _Omar E. Pol_, Nov 04 2013