A330103 Numbers whose prime-indices do not have weakly increasing numbers of prime factors, counted with multiplicity.

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

Author

Gus Wiseman, Dec 09 2019

Keywords

• nonn

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.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

The version where prime factors are counted without multiplicity is A330281.

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

Programs

Mathematica

Select[Range[1000],!OrderedQ[PrimeOmega/@PrimePi/@First/@FactorInteger[#]]&]

Extensions

Term 667 deleted by Gus Wiseman, Feb 07 2021