cp's OEIS Frontend

A377485 Irregular triangle where row n lists powers p^k of primes p | n such that p^k <= n and k > 0.

%I A377485 #7 Nov 01 2024 11:12:07
%S A377485 1,2,3,2,4,5,2,3,4,7,2,4,8,3,9,2,4,5,8,11,2,3,4,8,9,13,2,4,7,8,3,5,9,
%T A377485 2,4,8,16,17,2,3,4,8,9,16,19,2,4,5,8,16,3,7,9,2,4,8,11,16,23,2,3,4,8,
%U A377485 9,16,5,25,2,4,8,13,16,3,9,27,2,4,7,8,16,29
%N A377485 Irregular triangle where row n lists powers p^k of primes p | n such that p^k <= n and k > 0.
%C A377485 Row 1 is {1} by convention, since 1 is the empty product.
%H A377485 Michael De Vlieger, <a href="/A377485/b377485.txt">Table of n, a(n) for n = 1..12747</a> (rows n = 1..1500, flattened.)
%F A377485 Row n is { p^k : p | n, k = 1..floor(log n/log p) }, i.e., intersection of A246655 and row n of A162306.
%F A377485 Row p = {p} for prime p.
%F A377485 Row p^k = { p^j : j = 1..k } for prime p and k > 0.
%F A377485 A361373(n) = length of row n for n > 1.
%e A377485 Table of the first 12 rows:
%e A377485    n   row n
%e A377485   -------------------
%e A377485    1:  1;
%e A377485    2:  2;
%e A377485    3:  3:
%e A377485    4:  2, 4;
%e A377485    5:  5;
%e A377485    6:  2, 3, 4;
%e A377485    7:  7;
%e A377485    8:  2, 4, 8;
%e A377485    9:  3, 9;
%e A377485   10:  2, 4, 5, 8;
%e A377485   11: 11;
%e A377485   12:  2, 3, 4, 8, 9;
%t A377485 {{1}}~Join~Table[Union[Join @@ Map[#^Range[Floor@ Log[#, n]] &, FactorInteger[n][[All, 1]] ] ], {n, 2, 30}]
%Y A377485 Cf. A162306, A246655.
%K A377485 nonn,easy,tabf
%O A377485 1,2
%A A377485 _Michael De Vlieger_, Oct 29 2024