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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. 2

%I

%S 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,

%T 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,

%U 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

%N Irregular triangle T(n,k) read by rows: first row is 0, n-th row (n > 1) lists indices of distinct primes dividing n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F T(n,k) = A000720(A027748(n,k)).

%F T(n,1) = A055396(n).

%F T(n,A001221(n)) = A061395(n).

%e The irregular triangle begins:

%e 1: {0}

%e 2: {1}

%e 3: {2}

%e 4: {1}

%e 5: {3}

%e 6: {1, 2}

%e 7: {4}

%e 8: {1}

%e 9: {2}

%e 10: {1, 3}

%e 11: {5}

%e 12: {1, 2}

%t Flatten[Table[PrimePi[FactorInteger[n][[All, 1]]], {n, 1, 62}]]

%Y Cf. A000040, A000720, A001221 (row lengths), A027748, A055396, A061395, A066328 (row sums), A112798, A156061 (row products), A302170.

%K nonn,tabf

%O 1,3

%A _Ilya Gutkovskiy_, May 05 2018

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Last modified September 23 16:01 EDT 2020. Contains 337310 sequences. (Running on oeis4.)