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 A305936 #22 Aug 26 2018 20:13:40 %S A305936 1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,3,1,1,2,2,1,1,1,2,1,1,1,1,1,1,1,2, %T A305936 3,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,2,1,2,3,4,1,1,1,1,1,1,1,1,1,2,2,3,1, %U A305936 1,1,1,1,1,1,1,1,1,1,2,3,1,1,1,1,2,2,1 %N A305936 Irregular triangle whose n-th row is the multiset spanning an initial interval of positive integers with multiplicities equal to the n-th row of A296150 (the prime indices of n in weakly decreasing order). %e A305936 Row 90 is {1,1,1,2,2,3,3,4} because 90 = prime(3)*prime(2)*prime(2)*prime(1). %e A305936 Triangle begins: %e A305936 1: %e A305936 2: 1 %e A305936 3: 1 1 %e A305936 4: 1 2 %e A305936 5: 1 1 1 %e A305936 6: 1 1 2 %e A305936 7: 1 1 1 1 %e A305936 8: 1 2 3 %e A305936 9: 1 1 2 2 %e A305936 10: 1 1 1 2 %e A305936 11: 1 1 1 1 1 %e A305936 12: 1 1 2 3 %e A305936 13: 1 1 1 1 1 1 %t A305936 nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]]; %t A305936 Array[nrmptn,30] %Y A305936 Row lengths are A056239. Number of distinct elements in row n is A001222(n). Number of distinct multiplicities in row n is A001221(n). %Y A305936 Cf. A000041, A000720, A112798, A181821, A182850, A255906, A296150, A304464. %Y A305936 Cf. A318283, A318284, A318285, A318286, A318287, A318360, A318361, A318362, A318371. %K A305936 nonn,tabf %O A305936 1,5 %A A305936 _Gus Wiseman_, Aug 23 2018