A373411 - OEIS

%I #6 Jun 07 2024 08:04:47

%S 1,2,8,6,17,24,14,72,22,78,30,64,34,72,38,80,42,89,263,58,120,127,66,

%T 136,70,144,151,78,161,168,86,360,94,293,102,208,106,216,110,224,114,

%U 233,241,379,130,264,271,138,280,142,288,600,312,158,648,166,510,351

%N Sum of the n-th maximal antirun of squarefree numbers differing by more than one.

%C The length of this antirun is given by A373127.

%C An antirun of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by more than one.

%H Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>

%e Row-sums of:

%e    1

%e    2

%e    3  5

%e    6

%e    7 10

%e   11 13

%e   14

%e   15 17 19 21

%e   22

%e   23 26 29

%e   30

%e   31 33

%e   34

%e   35 37

%e   38

%e   39 41

%e   42

%e   43 46

%e   47 51 53 55 57

%t Total/@Split[Select[Range[100],SquareFreeQ],#1+1!=#2&]//Most

%Y The partial sums are a subset of A173143.

%Y Functional neighbors: A007674, A373127 (firsts A373128, sorted firsts A373200), A373404, A373405, A373408, A373412, A373413.

%Y A005117 lists the squarefree numbers, first differences A076259.

%Y A013929 lists the nonsquarefree numbers, first differences A078147.

%Y Cf. A025157, A049093, A061398, A077641, A077643, A112925, A112926, A143658, A372683, A373123, A373197, A373198.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jun 05 2024