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A330103 Numbers whose prime-indices do not have weakly increasing numbers of prime factors, counted with multiplicity. 13
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, 667, 693, 713, 714, 763, 767, 770, 779, 806, 817, 826, 833, 847, 861, 868, 871, 874, 884, 889, 893, 899, 924, 938 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..52.

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.

Cf. A001221, A001222, A056239, A112798, A302242, A330098, A330230, A330233.

Sequence in context: A235867 A274967 A229826 * A176278 A105998 A039444

Adjacent sequences:  A330100 A330101 A330102 * A330104 A330105 A330106

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 09 2019

STATUS

approved

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Last modified July 15 04:34 EDT 2020. Contains 335763 sequences. (Running on oeis4.)