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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).
44
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
1,5
EXAMPLE
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
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]
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).
Sequence in context: A300826 A373126 A334926 * A339790 A334924 A211111
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Aug 23 2018
STATUS
approved