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A378618 Sum of nonsquarefree numbers between prime(n) and prime(n+1).

%I A378618 #5 Dec 09 2024 11:02:37
%S A378618 0,4,0,17,12,16,18,20,104,0,68,40,0,89,199,110,60,127,68,72,151,161,
%T A378618 172,278,297,0,104,108,112,849,128,403,0,579,150,461,322,164,680,351,
%U A378618 180,561,192,196,198,819,648,449,228,232,470,240,1472,508,521,532,270
%N A378618 Sum of nonsquarefree numbers between prime(n) and prime(n+1).
%e A378618 The nonsquarefree numbers between prime(24) = 89 and prime(25) = 97 are {90, 92, 96}, so a(24) = 278.
%t A378618 Table[Total[Select[Range[Prime[n],Prime[n+1]],!SquareFreeQ[#]&]],{n,100}]
%Y A378618 For prime instead of nonsquarefree we have A001043.
%Y A378618 For composite instead of nonsquarefree we have A054265.
%Y A378618 Zeros are A068361.
%Y A378618 A000040 lists the primes, differences A001223, seconds A036263.
%Y A378618 A070321 gives the greatest squarefree number up to n.
%Y A378618 A071403 counts squarefree numbers up to prime(n), restriction of A013928.
%Y A378618 A120327 gives the least nonsquarefree number >= n.
%Y A378618 A378086 counts nonsquarefree numbers up to prime(n), restriction of A057627.
%Y A378618 For squarefree numbers (A005117, differences A076259) between primes:
%Y A378618 - length is A061398, zeros A068360
%Y A378618 - min is A112926, differences A378037
%Y A378618 - max is A112925, differences A378038
%Y A378618 - sum is A373197
%Y A378618 For nonsquarefree numbers (A013929, differences A078147) between primes:
%Y A378618 - length is A061399
%Y A378618 - min is A377783 (differences A377784), union A378040
%Y A378618 - max is A378032 (differences A378034), restriction of A378033 (differences A378036)
%Y A378618 - sum is A378618 (this)
%Y A378618 Cf. A007674, A045882, A053806, A067535, A072284, A073247, A179211, A224363, A373198, A377049, A377431.
%K A378618 nonn
%O A378618 1,2
%A A378618 _Gus Wiseman_, Dec 09 2024