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A357876
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The run-sums of the prime indices of n are not weakly increasing.
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6
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24, 45, 48, 80, 90, 96, 120, 135, 160, 168, 175, 180, 189, 192, 224, 240, 264, 270, 275, 288, 297, 312, 315, 320, 336, 350, 360, 378, 384, 405, 408, 448, 456, 480, 495, 525, 528, 539, 540, 550, 552, 560, 567, 576, 585, 594, 600, 624, 630, 637, 640, 672, 696
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OFFSET
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1,1
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COMMENTS
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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.
The sequence of runs of a sequence consists of its maximal consecutive constant subsequences when read left-to-right. For example, the runs of (2,2,1,1,1,3,2,2) are (2,2), (1,1,1), (3), (2,2), with sums (4,3,3,4).
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
24: {1,1,1,2}
45: {2,2,3}
48: {1,1,1,1,2}
80: {1,1,1,1,3}
90: {1,2,2,3}
96: {1,1,1,1,1,2}
120: {1,1,1,2,3}
135: {2,2,2,3}
160: {1,1,1,1,1,3}
168: {1,1,1,2,4}
175: {3,3,4}
180: {1,1,2,2,3}
189: {2,2,2,4}
192: {1,1,1,1,1,1,2}
For example, the prime indices of 24 are (1,1,1,2), with run-sums (3,2), which are not weakly increasing, so 24 is in the sequence.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], !LessEqual@@Total/@Split[primeMS[#]]&]
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CROSSREFS
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These are the indices of rows in A354584 that are not weakly increasing.
These partitions are counted by A357878.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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