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 A229945 Triangle read by rows in which row n lists the union of the primes <= n and the divisors of n. 0
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also row n lists the divisors of n and the primes < n that do not divide n, in increasing order. Also row n lists the nonprime divisors of n and the primes <= n, in increasing order. Note that if n is 1 or prime then row n lists the first A036234(n) terms of A008578. 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. LINKS EXAMPLE 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. 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. Written as an irregular triangle the sequence begins: 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, 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; 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; 1, 2, 3, 5, 7, 11, 13, 17; 1, 2, 3, 5, 6, 7, 9, 11, 13, 17, 18; 1, 2, 3, 5, 7, 11, 13, 17, 19; 1, 2, 3, 4, 5, 7, 10, 11, 13, 17, 19, 20; 1, 2, 3, 5, 7, 11, 13, 17, 19, 21; 1, 2, 3, 5, 7, 11, 13, 17, 19, 22; 1, 2, 3, 5, 7, 11, 13, 17, 19, 23; 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 17, 19, 23, 24; CROSSREFS Columns 1-3: A000012, A007395, A010701. Right border gives A000027. Cf. A000005, A000040, A000720, A008578, A027750, A036234, A046022. Sequence in context: A212721 A222417 A253573 * A119585 A195097 A181845 Adjacent sequences:  A229942 A229943 A229944 * A229946 A229947 A229948 KEYWORD nonn,tabf,less AUTHOR Omar E. Pol, Nov 04 2013 STATUS approved

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Last modified February 22 17:14 EST 2020. Contains 332140 sequences. (Running on oeis4.)