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A302170 Irregular triangle T(n,k) read by rows: first row is 1, n-th row (n > 1) lists distinct prime factors of n in decreasing order.

%I A302170 #26 Feb 16 2025 08:33:53
%S A302170 1,2,3,2,5,3,2,7,2,3,5,2,11,3,2,13,7,2,5,3,2,17,3,2,19,5,2,7,3,11,2,
%T A302170 23,3,2,5,13,2,3,7,2,29,5,3,2,31,2,11,3,17,2,7,5,3,2,37,19,2,13,3,5,2,
%U A302170 41,7,3,2,43,11,2,5,3,23,2,47,3,2,7,5,2,17,3,13,2,53,3,2,11,5,7,2,19,3,29,2,59,5,3,2,61,31,2
%N A302170 Irregular triangle T(n,k) read by rows: first row is 1, n-th row (n > 1) lists distinct prime factors of n in decreasing order.
%H A302170 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%F A302170 T(n,1) = A006530(n).
%F A302170 T(n,A001221(n)) = A020639(n).
%e A302170 The irregular triangle begins:
%e A302170 1:  {1}
%e A302170 2:  {2}
%e A302170 3:  {3}
%e A302170 4:  {2}
%e A302170 5:  {5}
%e A302170 6:  {3, 2}
%e A302170 7:  {7}
%e A302170 8:  {2}
%e A302170 9:  {3}
%e A302170 10: {5, 2}
%e A302170 11: {11}
%e A302170 12: {3, 2}
%t A302170 Flatten[Table[Reverse[FactorInteger[n][[All, 1]]], {n, 1, 62}]]
%o A302170 (Haskell)
%o A302170 a302170 n k = a302170_tabl !! (n-1) !! (k-1)
%o A302170 a302170_tabl = map a302170_row [1..]
%o A302170 a302170_row = reverse . a027748_row
%o A302170 -- _Brian Chess_, Sep 19 2022
%Y A302170 Cf. A001221 (row lengths), A006530, A008472 (row sums), A020639, A027746, A027748 (another version), A027750, A056538, A085307, A238689.
%K A302170 nonn,tabf
%O A302170 1,2
%A A302170 _Ilya Gutkovskiy_, Apr 02 2018