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A357188
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Numbers with (WLOG adjacent) prime indices x <= y such that the greatest prime factor of x is greater than the least prime factor of y.
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0
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35, 65, 70, 95, 105, 130, 140, 143, 145, 169, 175, 185, 190, 195, 209, 210, 215, 245, 247, 253, 260, 265, 280, 285, 286, 290, 305, 315, 319, 323, 325, 338, 350, 355, 370, 377, 380, 385, 390, 391, 395, 407, 418, 420, 429, 430, 435, 445, 455, 473, 475, 481, 490
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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 multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.
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LINKS
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EXAMPLE
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The terms and corresponding multisets of multisets:
35: {{2},{1,1}}
65: {{2},{1,2}}
70: {{},{2},{1,1}}
95: {{2},{1,1,1}}
105: {{1},{2},{1,1}}
130: {{},{2},{1,2}}
140: {{},{},{2},{1,1}}
143: {{3},{1,2}}
145: {{2},{1,3}}
169: {{1,2},{1,2}}
175: {{2},{2},{1,1}}
185: {{2},{1,1,2}}
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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], MatchQ[primeMS[#], {___, x_, y_, ___}/; Max@@primeMS[x]>Min@@primeMS[y]]&]
Select[Range[100], !LessEqual@@Join@@primeMS/@primeMS[#]&]
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CROSSREFS
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These are the positions of non-weakly increasing rows in A357139.
Cf. A000720, A001221, A001222, A007716, A275024, A302242, A302243, A302505, A324926, A325032, A325034.
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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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