A387892 Psi-deficient numbers: numbers k such that psi(k) < 2*k.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 86, 87, 88

Offset

1,2

Comments

From Amiram Eldar, Sep 11 2025: (Start)

A squarefree number is a term if and only if it is deficient (i.e., in A087246).

A number is a term if and only if its squarefree kernel (A007947) is deficient (i.e., in A087246).

If p_1, p_2, ..., p_k are the distinct prime factors of a number, then it is a term if and only if Product_{i=1..k} (1 + 1/p_i) < 2. (End)

Links

Table of n, a(n) for n=1..73.

Example

16 is in the sequence since psi(16) = 24 < 32.

Mathematica

psi[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors[n]}]; Select[Range[88], psi[#]<2# &] (* Stefano Spezia, Sep 11 2025 *)

Prog

(PARI) isok(k) = vecprod(apply(x -> 1 + 1/x, factor(k)[, 1])) < 2; \\ Amiram Eldar, Sep 11 2025

Crossrefs

Cf. A001615, A005100, A007947, A033845, A087246, A387893.

Sequence in context: A187390 A039215 A047253 * A248910 A254278 A204878

Adjacent sequences: A387889 A387890 A387891 * A387893 A387894 A387895

Keyword

nonn,easy

Author

S. I. Dimitrov, Sep 11 2025

Status

approved