A353869 Squarefree numbers k such that the Carmichael function A002322(k) divides the Dedekind psi A001615(k).

1, 2, 3, 6, 14, 15, 30, 35, 42, 65, 70, 78, 105, 119, 130, 182, 190, 195, 210, 238, 255, 357, 370, 377, 390, 418, 455, 510, 546, 570, 595, 663, 714, 754, 910, 969, 1045, 1110, 1118, 1131, 1190, 1254, 1326, 1330, 1365, 1547, 1558, 1615, 1785, 1885, 1887, 1938, 2090, 2190, 2261, 2262, 2470, 2590, 2639, 2730

Offset

1,2

Comments

If s,t are terms, then so is lcm(s,t); in particular, if s,t are coprime, then s*t is also a term. Primitive squarefree terms are listed in A353871.

Links

Aloe Poliszuk, Table of n, a(n) for n = 1..1000

Mathematica

psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); Select[Range[3000], SquareFreeQ[#] && Divisible[psi[#], CarmichaelLambda[#]] &] (* Amiram Eldar, May 09 2022 *)

Prog

(PARI) lpsi(n)=lcm(znstar(n)[2]) \\ A002322.
dpsi(n)=n*sumdivmult(n, d, issquarefree(d)/d) \\ A001615.
isok(n) = issquarefree(n) && (dpsi(n)%lpsi(n)==0); \\ Aloe Poliszuk, Nov 12 2025

Crossrefs

Intersection of A005117 and A353868.

Cf. A002322, A001615, A353870, A353871.

Sequence in context: A030733 A335288 A122839 * A258077 A121556 A123041

Adjacent sequences: A353866 A353867 A353868 * A353870 A353871 A353872

Keyword

nonn

Author

Max Alekseyev, May 08 2022

Status

approved