This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A294306 #16 Jan 06 2018 18:44:33
%S A294306 1,1,1,1,1,1,2,1,1,1,3,1,1,1,1,3,1,2,1,3,1,1,1,1,1,5,2,1,1,1,3,1,1,1,
%T A294306 3,1,1,4,1,1,1,5,2,1,1,1,1,1,5,2,1,3,1,1,3,1,1,1,1,1,1,7,3,1,2,1,3,1,
%U A294306 1,1,1,3,1,5,2,1,1,1,7,6,3,1,1,1,1,5
%N A294306 Irregular triangle read by rows: T(n, m) = total number of times the different values appear in row n of A280269, where 0 <= m <= A280274(n).
%C A294306 The numbers i in A162306(n) divide n^k with k >= 0; these k are listed in row n of A280269.
%C A294306 Row 1 = 1 and T(n, 0) = 1 for all n, since 1 is the empty product and divides n^0.
%C A294306 Row p = 1, 1, (row length = 2) since the only divisors of p are 1 and p; 1 | p^0, and p | p^1.
%C A294306 Row p^e = 1, e, since the only numbers in A162306(p^e) are 1 and p^k for 1 <= k <= e.
%C A294306 Row length of a(n) > 2 for n with omega(n) > 1.
%C A294306 Total of row n = A010846(n).
%C A294306 Sum of terms of T(n, m) with m <= 1 in row n = A000005(n).
%C A294306 Sum of terms of T(n, m) with m > 1 = A243822(n).
%C A294306 Terms in row n of A294306 start at 1, generally quickly rise to a maximum, then gradually decline at m = A280274(n).
%H A294306 Michael De Vlieger, <a href="/A294306/b294306.txt">Table of n, a(n) for n = 1..11355</a> (rows 1 <= n <= 2000).
%H A294306 Michael De Vlieger, <a href="/A294306/a294306.txt">A294306 and indices of records in A294306</a>.
%e A294306 Row n of A280269(10) = 0, 1, 2, 1, 3, 1, corresponding to A162306(10) = 1, 2, 4, 5, 8, 10, since 1 | 10^0, 2 | 10^1, 4 | 10^2, 5 | 10^1, 8 | 10^3, and 10 | 10^1. There is 1 zero, 3 ones, 1 two, and 1 three, thus a(10) = 1, 3, 1, 1. sum(a(10)) = A010846(10) = 6. Length of a(10) = A280274(10) + 1 = 4.
%e A294306 Triangle begins:
%e A294306 1: 1
%e A294306 2: 1 1
%e A294306 3: 1 1
%e A294306 4: 1 2
%e A294306 5: 1 1
%e A294306 6: 1 3 1
%e A294306 7: 1 1
%e A294306 8: 1 3
%e A294306 9: 1 2
%e A294306 10: 1 3 1 1
%e A294306 11: 1 1
%e A294306 12: 1 5 2
%e A294306 13: 1 1
%e A294306 14: 1 3 1 1
%e A294306 15: 1 3 1
%e A294306 16: 1 4
%e A294306 17: 1 1
%e A294306 18: 1 5 2 1 1
%e A294306 19: 1 1
%e A294306 20: 1 5 2
%e A294306 ...
%t A294306 Table[Tally[#][[All, -1]] &@ Map[SelectFirst[Range[0, Floor@ Log2@ n], Function[k, Divisible[n^k, #]]] &, Select[Range@ n, PowerMod[n, Floor@ Log2@ n, #] == 0 &]], {n, 32}] // Flatten (* _Michael De Vlieger_, Oct 30 2017 *)
%Y A294306 Cf. A000005, A010846, A162306, A243822, A280269, A280274.
%K A294306 nonn,tabf
%O A294306 1,7
%A A294306 _Michael De Vlieger_, Oct 30 2017