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A330103
Numbers whose prime-indices do not have weakly increasing numbers of prime factors, counted with multiplicity.
15
77, 119, 154, 217, 221, 231, 238, 287, 308, 357, 385, 403, 413, 434, 437, 442, 462, 469, 476, 533, 539, 551, 574, 581, 589, 595, 616, 651, 663, 693, 713, 714, 763, 767, 770, 779, 806, 817, 826, 833, 847, 861, 868, 871, 874, 884, 889, 893, 899, 924, 938
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.
LINKS
EXAMPLE
The sequence of terms together with their corresponding multisets of multisets begins:
77: {{1,1},{3}}
119: {{1,1},{4}}
154: {{},{1,1},{3}}
217: {{1,1},{5}}
221: {{1,2},{4}}
231: {{1},{1,1},{3}}
238: {{},{1,1},{4}}
287: {{1,1},{6}}
308: {{},{},{1,1},{3}}
357: {{1},{1,1},{4}}
385: {{2},{1,1},{3}}
For example, 385 has prime indices {3,4,5} with numbers of prime factors (1,2,1), which is not weakly increasing, so 385 is in the sequence.
MATHEMATICA
Select[Range[1000], !OrderedQ[PrimeOmega/@PrimePi/@First/@FactorInteger[#]]&]
CROSSREFS
The version where prime factors are counted without multiplicity is A330281.
Sequence in context: A235867 A274967 A229826 * A176278 A105998 A039444
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 09 2019
EXTENSIONS
Term 667 deleted by Gus Wiseman, Feb 07 2021
STATUS
approved