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).

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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 2, 1

Offset: 1

Author

Gus Wiseman, Aug 23 2018

Keywords

• nonn
• tabf

Examples

			Row 90 is {1,1,1,2,2,3,3,4} because 90 = prime(3)*prime(2)*prime(2)*prime(1).
Triangle begins:
   1:
   2:  1
   3:  1  1
   4:  1  2
   5:  1  1  1
   6:  1  1  2
   7:  1  1  1  1
   8:  1  2  3
   9:  1  1  2  2
  10:  1  1  1  2
  11:  1  1  1  1  1
  12:  1  1  2  3
  13:  1  1  1  1  1  1
		

Crossrefs

Row lengths are A056239. Number of distinct elements in row n is A001222(n). Number of distinct multiplicities in row n is A001221(n).

Cf. A000041, A000720, A112798, A181821, A182850, A255906, A296150, A304464.

Cf. A318283, A318284, A318285, A318286, A318287, A318360, A318361, A318362, A318371.

Programs

Mathematica

nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
Array[nrmptn,30]