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

Author

Leroy Quet, Sep 06 2000

Keywords

• nonn
• easy

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)

Examples

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

Links

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

Crossrefs

Cf. A056819, A377484.

A377949 is a subsequence.

Similar sequences: A355331, A377950, A377952.

Programs

Mathematica

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

PARI

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