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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.

%I A304038 #8 Feb 16 2025 08:33:54
%S A304038 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 A304038 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 A304038 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 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.
%H A304038 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%H A304038 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A304038 T(n,k) = A000720(A027748(n,k)).
%F A304038 T(n,1) = A055396(n).
%F A304038 T(n,A001221(n)) = A061395(n).
%e A304038 The irregular triangle begins:
%e A304038 1:  {0}
%e A304038 2:  {1}
%e A304038 3:  {2}
%e A304038 4:  {1}
%e A304038 5:  {3}
%e A304038 6:  {1, 2}
%e A304038 7:  {4}
%e A304038 8:  {1}
%e A304038 9:  {2}
%e A304038 10: {1, 3}
%e A304038 11: {5}
%e A304038 12: {1, 2}
%t A304038 Flatten[Table[PrimePi[FactorInteger[n][[All, 1]]], {n, 1, 62}]]
%Y A304038 Cf. A000040, A000720, A001221 (row lengths), A027748, A055396, A061395, A066328 (row sums), A112798, A156061 (row products), A302170.
%K A304038 nonn,tabf
%O A304038 1,3
%A A304038 _Ilya Gutkovskiy_, May 05 2018