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A321144
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Irregular triangle where T(n,k) is the number of divisors of n whose prime indices sum to k.
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3
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1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0
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OFFSET
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1,45
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COMMENTS
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The rows are all palindromes.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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EXAMPLE
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Triangle begins:
1
1 1
1 0 1
1 1 1
1 0 0 1
1 1 1 1
1 0 0 0 1
1 1 1 1
1 0 1 0 1
1 1 0 1 1
1 0 0 0 0 1
1 1 2 1 1
1 0 0 0 0 0 1
1 1 0 0 1 1
1 0 1 1 0 1
1 1 1 1 1
1 0 0 0 0 0 0 1
1 1 1 1 1 1
1 0 0 0 0 0 0 0 1
1 1 1 1 1 1
1 0 1 0 1 0 1
1 1 0 0 0 1 1
1 0 0 0 0 0 0 0 0 1
1 1 2 2 1 1
1 0 0 1 0 0 1
1 1 0 0 0 0 1 1
1 0 1 0 1 0 1
1 1 1 0 1 1 1
1 0 0 0 0 0 0 0 0 0 1
1 1 1 2 1 1 1
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]
Table[Count[Total/@primeMS/@Divisors[n], k], {n, 20}, {k, 0, Total[primeMS[n]]}]
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CROSSREFS
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Row lengths are A056239. Number of nonzero entries in row n is A299701(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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