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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
Eric Weisstein's World of Mathematics, Distinct Prime Factors
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
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.)