A056954 Numbers k such that k^2 divides A056819(k).

1, 30, 60, 90, 105, 120, 132, 144, 168, 180, 210, 240, 252, 264, 280, 336, 360, 380, 396, 420, 495, 504, 520, 528, 540, 546, 552, 560, 612, 616, 630, 660, 720, 728, 756, 760, 792, 840, 858, 870, 900, 924, 990, 1008, 1040, 1050, 1056, 1080, 1092, 1104

Offset

1,2

Comments

From Amiram Eldar, Nov 12 2024: (Start)

Equivalently, numbers k that divide A377484(k) = Product_{d|k, d>1} (d - 1).

After the first term a(1) = 1, the next odd term is a(5) = 105, the next term that is coprime to 6 is a(228) = 6545, and the next term that is coprime to 30 is a(574) = 19019. (End)

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

30 is a term because 30^2 divides A056819(30) = 5320224000.

Mathematica

Select[Range[1000], Divisible[Times @@ (Rest@ Divisors[#] - 1), #] &] (* Amiram Eldar, Nov 12 2024 *)

Prog

(PARI) is(k) = if(k == 1, 1, my(d = divisors(k)); !(prod(i = 2, #d, d[i]-1) % k)); \\ Amiram Eldar, Nov 12 2024

Crossrefs

Cf. A056819, A377484.

A377949 is a subsequence.

Similar sequences: A355331, A377950, A377952.

Sequence in context: A377259 A222618 A325992 * A378885 A377952 A246947

Adjacent sequences: A056951 A056952 A056953 * A056955 A056956 A056957

Keyword

nonn,easy

Author

Leroy Quet, Sep 06 2000

Status

approved