A378084 Nonsquarefree numbers not appearing in A377783 (least nonsquarefree number > prime(n)).

9, 25, 27, 28, 36, 45, 49, 50, 52, 56, 64, 76, 81, 88, 92, 96, 99, 100, 117, 120, 121, 124, 125, 126, 135, 136, 144, 147, 148, 153, 156, 162, 169, 171, 172, 176, 188, 189, 204, 207, 208, 216, 220, 225, 236, 243, 244, 245, 248, 250, 256, 261, 268, 275, 276, 280

Offset: 1

Author

Gus Wiseman, Nov 23 2024

Keywords

• nonn

Comments

Warning: do not confuse with A377784.

Examples

			The terms together with their prime indices begin:
    9: {2,2}
   25: {3,3}
   27: {2,2,2}
   28: {1,1,4}
   36: {1,1,2,2}
   45: {2,2,3}
   49: {4,4}
   50: {1,3,3}
   52: {1,1,6}
   56: {1,1,1,4}
   64: {1,1,1,1,1,1}
   76: {1,1,8}
   81: {2,2,2,2}
   88: {1,1,1,5}
   92: {1,1,9}
   96: {1,1,1,1,1,2}
		

Crossrefs

Disjoint from A377783 (union A378040), first-differences A377784.

Appearing once: A378082.

Appearing twice: A378083.

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers.

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

A061398 counts squarefree numbers between primes (sums A337030), zeros A068360.

A061399 counts nonsquarefree numbers between primes (sums A378086), zeros A068361.

A070321 gives the greatest squarefree number up to n.

A112925 gives least squarefree number > prime(n), differences A378038.

A112926 gives greatest squarefree number < prime(n), differences A378037.

A120327 (union A162966) gives least nonsquarefree number >= n, differences A378039.

A377046 encodes k-differences of nonsquarefree numbers, zeros A377050.

Cf. A053797, A053806, A072284, A224363, A377430, A377431, A378032, A378033.

Programs

Mathematica

nn=100;
y=Table[NestWhile[#+1&,Prime[n],SquareFreeQ[#]&],{n,nn}];
Complement[Select[Range[Prime[nn]],!SquareFreeQ[#]&],y]

Formula

Complement of A378040 in A013929.