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 A283866 #12 Mar 18 2017 11:33:54
%S A283866 0,1,1,3,1,4,2,1,6,3,7,2,1,9,5,1,7,2,4,2,10,1,14,7,1,13,3,4,2,11,2,1,
%T A283866 17,8,3,11,2,6,13,3,1,21,13,7,1,15,7,2,16,2,4,2,24,13,1,16,2,7,2,21,6,
%U A283866 1,28,15,5,1,18,3,9,5,16,2,1,28,14,3,22,8
%N A283866 Multiplicities of prime factors of A243103(n).
%C A283866 Irregular triangle T(n,m) of multiplicities of the product of the numbers 1 <= k <= n | n^e with e >= 0.
%C A283866 Count of instances of primes p|n among the prime factors of all numbers 1 <= k <= n.
%C A283866 A243103(n) = Product of row n of A162306; prime divisors of A243103(n) = prime divisors of n = A027748(n).
%C A283866 a(1) = 0; a(p) = 1 for prime p. For prime powers p^e with e>=0, a(p^e) = A000217(e).
%H A283866 Michael De Vlieger, <a href="/A283866/b283866.txt">Table of n, a(n) for n = 1..11739</a> (rows 1 <= n <= 5000)
%e A283866 Row 12 = 9,5 because the numbers 1 <= k <= 12 | 12^e with e>=0, {1,2,3,4,6,8,9,12} and these have the prime decompositions:
%e A283866 1 = 1
%e A283866 2 = 2^1
%e A283866 3 = 3^1
%e A283866 4 = 2^2
%e A283866 6 = 2^1 * 3^1
%e A283866 8 = 2^3
%e A283866 9 = 3^2
%e A283866 12 = 2^2 * 3^1
%e A283866 Adding the multiplicities of the factors of 12 for each of these gives us 9,5.
%e A283866 Row 42 = 28,15,5 since A243103(42) = 64736452901018271744 = 2^28 * 3^15 * 7^5.
%e A283866 Relationship of first 12 rows of a(n) with A027748(n) and A243103(n):
%e A283866 n A027748(n) a(n) A243103(n)
%e A283866 1 1 0 1 = 1^0
%e A283866 2 2 1 2 = 2^1
%e A283866 3 3 1 3 = 3^1
%e A283866 4 2 3 8 = 2^3
%e A283866 5 5 1 5 = 5^1
%e A283866 6 2,3 4,2 144 = 2^4 * 3^2
%e A283866 7 7 1 7 = 7^1
%e A283866 8 2 6 64 = 2^6
%e A283866 9 3 3 27 = 3^3
%e A283866 10 2,5 7,2 3200 = 2^7 * 5*2
%e A283866 11 11 1 11 = 11^1
%e A283866 12 2,3 9,5 124416 = 2^9 * 3^5
%e A283866 ...
%e A283866 T(n,m) for n = primorial p_x# = A002110(x), with horizontal axis the multiplicity pertaining to prime(m):
%e A283866 x 2 3 5 7 11 13 17 19
%e A283866 1 1
%e A283866 2 4 2
%e A283866 3 21 13 7
%e A283866 4 118 63 36 26
%e A283866 5 625 351 200 147 101
%e A283866 6 2982 1694 1003 753 537 477
%e A283866 7 14131 8128 4905 3733 2693 2404 2025
%e A283866 8 64332 37274 22763 17448 12744 11450 9698 9078
%e A283866 ...
%t A283866 Table[With[{m = Floor@ Log2@ n}, Values@ Merge[Association /@ Map[#1 -> #2 & @@ # &, FactorInteger@ Rest@ Select[Range@ n, PowerMod[n, m, #] == 0 &], {2}], Total]] /. {} -> {0}, {n, 50}] // Flatten (* _Michael De Vlieger_, Mar 17 2017, Version 10 *)
%Y A283866 Cf. A001221 (row lengths), A027748, A243103, A010846 (number of 1 <= m <= n | n^e), A162306 (list of 1 <= m <= n | n^e), A124010 (multiplicities of primes in n).
%K A283866 nonn,tabf,easy
%O A283866 1,4
%A A283866 _Michael De Vlieger_, Mar 17 2017