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

1,1

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

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

Example

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.

Mathematica

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

Crossrefs

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

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

Sequence in context: A266237 A371899 A159565 * A345512 A048931 A052478

Adjacent sequences: A330278 A330279 A330280 * A330282 A330283 A330284

Keyword

nonn

Author

Gus Wiseman, Dec 10 2019

Status

approved