A378083 Nonsquarefree numbers appearing exactly twice in A377783 (least nonsquarefree number > prime(n)).

4, 8, 32, 44, 104, 140, 284, 464, 572, 620, 644, 824, 860, 1232, 1292, 1304, 1484, 1700, 1724, 1880, 2084, 2132, 2240, 2312, 2384, 2660, 2732, 2804, 3392, 3464, 3560, 3920, 3932, 4004, 4220, 4244, 4424, 4640, 4724, 5012, 5444, 5480, 5504, 5660, 6092, 6200

Offset: 1

Author

Gus Wiseman, Nov 23 2024

Keywords

• nonn

Comments

Warning: do not confuse with A377783.

Examples

			The terms together with their prime indices begin:
     4: {1,1}
     8: {1,1,1}
    32: {1,1,1,1,1}
    44: {1,1,5}
   104: {1,1,1,6}
   140: {1,1,3,4}
   284: {1,1,20}
   464: {1,1,1,1,10}
   572: {1,1,5,6}
   620: {1,1,3,11}
   644: {1,1,4,9}
   824: {1,1,1,27}
   860: {1,1,3,14}
  1232: {1,1,1,1,4,5}
		

Crossrefs

Subset of A377783 (union A378040, diffs A377784), restriction of A120327 (diffs A378039).

Terms appearing once are A378082.

Terms not appearing at all are A378084.

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers.

A013929 lists the nonsquarefree numbers, differences A078147.

A061398 counts squarefree numbers between primes, zeros A068360.

A061399 counts nonsquarefree numbers between primes, zeros A068361.

A071403(n) = A013928(prime(n)) counts squarefree numbers < prime(n).

A378086(n) = A057627(prime(n)) counts nonsquarefree numbers < prime(n).

Cf. A112926 (diffs A378037), opposite A112925 (diffs A378038).

Cf. A378032 (diffs A378034), restriction of A378033 (diffs A378036).

Cf. A053797, A053806, A070321, A072284, A112929, A120992, A224363, A337030, A377430, A377431, A377703.

Programs

Mathematica

y=Table[NestWhile[#+1&,Prime[n],SquareFreeQ[#]&],{n,1000}];
Select[Union[y],Count[y,#]==2&]