A330281 - OEIS

%I #8 Feb 07 2021 06:25:42

%S 221,247,299,403,442,494,533,598,663,689,741,767,806,871,884,897,899,

%T 988,1066,1079,1105,1189,1196,1209,1235,1261,1326,1339,1378,1417,1482,

%U 1495,1517,1534,1537,1547,1599,1612,1651,1703,1711,1729,1742,1768,1794,1798

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

%C 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.

%H Amiram Eldar, <a href="/A330281/b330281.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence of terms together with their prime indices begins:

%e    221: {6,7}

%e    247: {6,8}

%e    299: {6,9}

%e    403: {6,11}

%e    442: {1,6,7}

%e    494: {1,6,8}

%e    533: {6,13}

%e    598: {1,6,9}

%e    663: {2,6,7}

%e    689: {6,16}

%e    741: {2,6,8}

%e    767: {6,17}

%e    806: {1,6,11}

%e    871: {6,19}

%e    884: {1,1,6,7}

%e 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.

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

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

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Dec 10 2019