cp's OEIS Frontend

A375398 Numbers k such that the minima of maximal anti-runs in the weakly increasing sequence of prime factors of k (with multiplicity) are distinct.

%I A375398 #8 Aug 17 2024 09:02:18
%S A375398 1,2,3,5,6,7,10,11,13,14,15,17,18,19,21,22,23,26,29,30,31,33,34,35,37,
%T A375398 38,39,41,42,43,46,47,50,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,
%U A375398 74,75,77,78,79,82,83,85,86,87,89,90,91,93,94,95,97,98
%N A375398 Numbers k such that the minima of maximal anti-runs in the weakly increasing sequence of prime factors of k (with multiplicity) are distinct.
%C A375398 First differs from A375402 in lacking 20.
%C A375398 An anti-run is a sequence with no adjacent equal parts.
%C A375398 The minima of maximal anti-runs in a sequence are obtained by splitting it into maximal anti-run subsequences and taking the least term of each.
%C A375398 Note the prime factors can alternatively be taken in weakly decreasing order.
%H A375398 Gus Wiseman, <a href="/A374629/a374629.txt">Sequences counting and ranking compositions by their leaders (for six types of runs)</a>.
%e A375398 The prime factors of 300 are {2,2,3,5,5}, with maximal anti-runs ((2),(2,3,5),(5)), with minima (2,2,5), so 300 is not in the sequence.
%e A375398 The prime factors of 450 are {2,3,3,5,5}, with maximal anti-runs ((2,3),(3,5),(5)), with minima (2,3,5), so 450 is in the sequence.
%t A375398 Select[Range[100],UnsameQ@@Min /@ Split[Flatten[ConstantArray@@@FactorInteger[#]],UnsameQ]&]
%Y A375398 A version for compositions is A374638, counted by A374518.
%Y A375398 These are positions of strict rows in A375128, sums A374706, ranks A375400.
%Y A375398 Partitions (or reversed partitions) of this type are counted by A375134.
%Y A375398 For identical instead of distinct we have A375396, counted by A115029.
%Y A375398 The complement is A375399, counted by A375404.
%Y A375398 For maxima instead of minima we have A375402, counted by A375133.
%Y A375398 The complement for maxima is A375403, counted by A375401.
%Y A375398 A000041 counts integer partitions, strict A000009.
%Y A375398 A003242 counts anti-run compositions, ranks A333489.
%Y A375398 A number's prime factors (A027746, reverse A238689) have sum A001414, min A020639, max A006530.
%Y A375398 A number's prime indices (A112798, reverse A296150) have sum A056239, min A055396, max A061395.
%Y A375398 Both have length A001222, distinct A001221.
%Y A375398 Cf. A034296, A036785, A046660, A065200, A065201, A358836, A374632, A374761, A374767, A374768, A375136.
%K A375398 nonn
%O A375398 1,2
%A A375398 _Gus Wiseman_, Aug 16 2024