A302838 Values of A000010(m) where the value and least solution m are both divisible by the number of solutions of A000010(m) = A000010(x).

20, 204, 444, 500, 564, 588, 684, 744, 1160, 1284, 1416, 1644, 1704, 1764, 1812, 2124, 2172, 2480, 2604, 2844, 2892, 2964, 3084, 3156, 3192, 3320, 3324, 3396, 3492, 3560, 3576, 3756, 3972, 4116, 4164, 4404, 4476, 4520, 4572, 4740, 4764, 5004, 5352, 5360, 5364, 5496, 5532, 5604, 5772, 5840, 6200

Offset

1,1

Comments

For known terms the number of solutions is prime.

All known terms are nonsquarefree.

The terms of this sequence that have a nonprime number of solutions are 195200, 248000, 941600, 980784, ... . There are no squarefree terms below 10^8. - Amiram Eldar, Nov 16 2024

Links

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

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Formula

0 = A000010(m) mod #{A000010(m) = A000010(x)} = A000010(m) mod min({A000010(m) = A000010(x)}).

Example

20 is a term because 25 is the least solution of 20 = A000010(x) and the number of solutions 5, divides 20 and 25.
204 is a term because 309 is the least solution of 204 = A000010(x) and the number of solutions 3, divides 204 and 309.
1764 is a term because 2107 is the least solution of 1764 = A000010(x) and the number of solutions 7, divides 1764 and 2107.
10 is not a term because 11 is the least solution of 10 = A000010(x) and the number of solutions 2, does not divide 10 and 11.

Prog

(PARI) is(k) = {my(ns = invphiNum(k)); ns > 0 && !(k % ns) && !(invphiMin(k) % ns); } \\ Amiram Eldar, Nov 16 2024, using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000010, A002202.

Sequence in context: A099197 A041766 A121088 * A302921 A334692 A325474

Adjacent sequences: A302835 A302836 A302837 * A302839 A302840 A302841

Keyword

nonn

Author

Torlach Rush, Apr 13 2018

Status

approved