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 A260684 Irregular triangular array read by rows.  Row n gives the primes in the prime factorization of n! that have exponent of 1. 1
 2, 2, 3, 3, 3, 5, 5, 5, 7, 5, 7, 5, 7, 7, 7, 11, 7, 11, 7, 11, 13, 11, 13, 11, 13, 11, 13, 11, 13, 17, 11, 13, 17, 11, 13, 17, 19, 11, 13, 17, 19, 11, 13, 17, 19, 13, 17, 19, 13, 17, 19, 23, 13, 17, 19, 23, 13, 17, 19, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS For any prime p in row n, binomial(n,p)==1 (mod p).  This is a consequence of Sylow's (3rd) Theorem.  For these primes the number of p-Sylow subgroups in S_n is binomial(n,p)*(p-2)!.  By Wilson's Theorem (p-2)!==1 (mod p) so that binomial(n,p)==1 (mod p). LINKS Alois P. Heinz, Rows n = 2..500, flattened EXAMPLE 2; 2, 3; 3; 3, 5; 5; 5, 7; 5, 7; 5, 7; 7; 7, 11; 7, 11; 7, 11, 13; 11, 13; 11, 13; 11, 13; 11, 13, 17; 11, 13, 17; 11, 13, 17, 19; 11, 13, 17, 19; MATHEMATICA Table[Select[FactorInteger[n!], #[[2]] == 1 &][[All, 1]], {n, 2, 20}] // Grid CROSSREFS Cf. A000142. The last entry in each row gives A007917. Sequence in context: A108035 A202503 A049747 * A029093 A301541 A240519 Adjacent sequences:  A260681 A260682 A260683 * A260685 A260686 A260687 KEYWORD nonn,tabf AUTHOR Geoffrey Critzer, Nov 15 2015 STATUS approved

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Last modified December 4 00:33 EST 2020. Contains 338920 sequences. (Running on oeis4.)