A378037 - OEIS

%I #8 Dec 04 2024 15:44:10

%S 2,1,4,3,1,5,2,5,4,3,5,4,4,5,4,6,1,7,4,1,8,3,6,10,1,3,4,1,4,15,4,5,3,

%T 10,3,4,7,5,4,7,1,11,1,5,2,12,13,3,1,5,6,5,7,5,7,6,2,5,4,3,10,14,4,1,

%U 4,16,5,10,4,1,8,8,4,7,4,5,8,4,8,11,1,11,1

%N First differences of A112926 (smallest squarefree integer > prime(n)).

%t Differences[Table[NestWhile[#+1&,Prime[n]+1,!SquareFreeQ[#]&],{n,100}]]

%Y First differences of A112926, restriction of A067535, differences A378087.

%Y For prime powers we have A377703.

%Y The nonsquarefree version is A377784 (differences of A377783), restriction of A378039.

%Y The nonsquarefree opposite is A378034, first differences of A378032.

%Y The opposite is A378038, differences of A112925.

%Y The unrestricted opposite is A378085 except first term, differences of A070321.

%Y A000040 lists the primes, differences A001223, seconds A036263.

%Y A005117 lists the squarefree numbers.

%Y A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.

%Y A061398 counts squarefree numbers between primes, zeros A068360.

%Y A061399 counts nonsquarefree numbers between primes, zeros A068361.

%Y Cf. A007674, A013928, A045882, A053797, A053806, A072284, A073247, A120327, A280892, A378036, A378040, A378084.

%K nonn

%O 1,1

%A _Gus Wiseman_, Dec 04 2024