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A357188
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.
0
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
OFFSET
1,1
COMMENTS
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}}.
EXAMPLE
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}}
MATHEMATICA
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[#]&]
CROSSREFS
These are the positions of non-weakly increasing rows in A357139.
A000961 lists prime powers.
A003963 multiples prime indices.
A056239 adds up prime indices.
Sequence in context: A338244 A250764 A362198 * A350344 A245274 A092256
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 30 2022
STATUS
approved