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A377488 Irregular triangle r ead by rows where row n lists powers p^k for primes p | n such that k = floor(log n/log p).

%I A377488 #8 Nov 01 2024 23:52:24
%S A377488 1,2,3,4,5,3,4,7,8,9,5,8,11,8,9,13,7,8,5,9,16,17,9,16,19,5,16,7,9,11,
%T A377488 16,23,9,16,25,13,16,27,7,16,29,16,25,27,31,32,11,27,17,32,7,25,27,32,
%U A377488 37,19,32,13,27,25,32,41,7,27,32,43,11,32,25,27,23,32
%N A377488 Irregular triangle r ead by rows where row n lists powers p^k for primes p | n such that k = floor(log n/log p).
%C A377488 Row 1 is {1} by convention, since 1 is the empty product.
%H A377488 Michael De Vlieger, <a href="/A377488/b377488.txt">Table of n, a(n) for n = 1..11739</a> (rows n = 1..5000, flattened)
%H A377488 Michael De Vlieger, <a href="/A377488/a377488.png">Log log scatterplot of rows n of this sequence</a>, n = 1.2^20 (2996045 terms).
%F A377488 Row n is { p^k : p | n, k = floor(log n/log p) }.
%F A377488 Row p^k = { p^k } for prime p and k > 0.
%F A377488 A001221(n) = length of row n for n > 1.
%F A377488 A064446(n) = product of row n.
%F A377488 A339378(n) = sum of row n for n > 1.
%e A377488 Table of the first 12 rows:
%e A377488    1:  1;
%e A377488    2:  2;
%e A377488    3:  3:
%e A377488    4:  4;
%e A377488    5:  5;
%e A377488    6:  3, 4;
%e A377488    7:  7;
%e A377488    8:  8;
%e A377488    9:  9;
%e A377488   10:  5, 8;
%e A377488   11: 11;
%e A377488   12:  8, 9.
%t A377488 {{1}}~Join~Table[Union[Join @@ Map[#^Range[Floor@ Log[#, n]] &, FactorInteger[n][[All, 1]] ] ], {n, 2, 30}]
%Y A377488 Cf. A001221, A064446, A339378, A377485.
%K A377488 nonn,tabf,easy
%O A377488 1,2
%A A377488 _Michael De Vlieger_, Nov 01 2024