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 A304038 Irregular triangle T(n,k) read by rows: first row is 0, n-th row (n > 1) lists indices of distinct primes dividing n. 42
 0, 1, 2, 1, 3, 1, 2, 4, 1, 2, 1, 3, 5, 1, 2, 6, 1, 4, 2, 3, 1, 7, 1, 2, 8, 1, 3, 2, 4, 1, 5, 9, 1, 2, 3, 1, 6, 2, 1, 4, 10, 1, 2, 3, 11, 1, 2, 5, 1, 7, 3, 4, 1, 2, 12, 1, 8, 2, 6, 1, 3, 13, 1, 2, 4, 14, 1, 5, 2, 3, 1, 9, 15, 1, 2, 4, 1, 3, 2, 7, 1, 6, 16, 1, 2, 3, 5, 1, 4, 2, 8, 1, 10, 17, 1, 2, 3, 18, 1, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..100. Eric Weisstein's World of Mathematics, Distinct Prime Factors Index entries for sequences computed from indices in prime factorization FORMULA T(n,k) = A000720(A027748(n,k)). T(n,1) = A055396(n). T(n,A001221(n)) = A061395(n). EXAMPLE The irregular triangle begins: 1: {0} 2: {1} 3: {2} 4: {1} 5: {3} 6: {1, 2} 7: {4} 8: {1} 9: {2} 10: {1, 3} 11: {5} 12: {1, 2} MATHEMATICA Flatten[Table[PrimePi[FactorInteger[n][[All, 1]]], {n, 1, 62}]] CROSSREFS Cf. A000040, A000720, A001221 (row lengths), A027748, A055396, A061395, A066328 (row sums), A112798, A156061 (row products), A302170. Sequence in context: A341049 A144113 A370329 * A366113 A301983 A373889 Adjacent sequences: A304035 A304036 A304037 * A304039 A304040 A304041 KEYWORD nonn,tabf AUTHOR Ilya Gutkovskiy, May 05 2018 STATUS approved

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Last modified July 25 05:51 EDT 2024. Contains 374586 sequences. (Running on oeis4.)