A380413 Terms appearing twice in A378086 (number of nonsquarefree numbers < prime(n)).

0, 1, 11, 14, 39, 53, 109, 179, 222, 240, 251, 319, 337, 481, 505, 508, 578, 664, 674, 738, 818, 835, 877, 905, 933, 1041, 1069, 1098, 1325, 1352, 1392, 1535, 1539, 1567, 1652, 1663, 1732, 1817, 1849, 1960, 2134, 2148, 2158, 2220, 2387, 2428, 2457, 2622, 2625

Offset: 1

Author

Gus Wiseman, Feb 06 2025

Keywords

• nonn

Crossrefs

A000040 lists the primes, differences A001223, seconds A036263.

A005117 lists the squarefree numbers, differences A076259.

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

A061399 counts nonsquarefree integers between primes, see A068361, A061398, A068360, A377783, A378086.

A070321 gives the greatest squarefree number up to n.

A071403 counts squarefree numbers < prime(n), see A373198, A337030.

A112925 gives the greatest squarefree number between primes, least A112926.

Cf. A057627, A065890, A378032 (differences A378034), A378033 (differences A378036).

Cf. A072284, A120327, A224363, A378040, A378082, A378084.

Programs

Mathematica

y=Table[Length[Select[Range[Prime[n]],!SquareFreeQ[#]&]],{n,100}];
Select[Most[Union[y]],Count[y,#]==2&]

Formula

a(n) = A378086(A068361(n)) = A378086(A068361(n)+1).