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A305936
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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).
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44
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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
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OFFSET
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1,5
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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]
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CROSSREFS
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Row lengths are A056239. Number of distinct elements in row n is A001222(n). Number of distinct multiplicities in row n is A001221(n).
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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