A330281 Numbers whose prime-indices do not have weakly increasing numbers of distinct prime factors.

221, 247, 299, 403, 442, 494, 533, 598, 663, 689, 741, 767, 806, 871, 884, 897, 899, 988, 1066, 1079, 1105, 1189, 1196, 1209, 1235, 1261, 1326, 1339, 1378, 1417, 1482, 1495, 1517, 1534, 1537, 1547, 1599, 1612, 1651, 1703, 1711, 1729, 1742, 1768, 1794, 1798

Offset: 1

Author

Gus Wiseman, Dec 10 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 prime indices begins:
   221: {6,7}
   247: {6,8}
   299: {6,9}
   403: {6,11}
   442: {1,6,7}
   494: {1,6,8}
   533: {6,13}
   598: {1,6,9}
   663: {2,6,7}
   689: {6,16}
   741: {2,6,8}
   767: {6,17}
   806: {1,6,11}
   871: {6,19}
   884: {1,1,6,7}
For example, 884 has prime indices {1,1,6,7} with numbers of distinct prime factors (0,0,2,1), which is not weakly increasing, so 884 belongs to the sequence.
		

Links

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

Crossrefs

The version where prime factors are counted with multiplicity is A330103.

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

Programs

Mathematica

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