A354715 Numbers k such that the number of divisors of k divides k-2.

1, 2, 6, 10, 14, 20, 22, 26, 32, 34, 38, 42, 44, 46, 50, 58, 62, 66, 68, 74, 82, 86, 92, 94, 98, 106, 112, 114, 116, 118, 122, 130, 134, 138, 142, 146, 154, 158, 162, 164, 166, 170, 178, 186, 188, 194, 202, 206, 210, 212, 214, 218, 226, 236, 242, 250, 254, 258, 262, 266, 272, 274, 278, 282

Offset: 1

Author

Max Alekseyev, Jun 03 2022

Keywords

• nonn

Comments

Numbers k such that k == 2 (mod A000005(k)).

Odd terms are squares. Next odd term after 1 is 5^16 * 29^6 = 90762835845947265625 (cf. A354716).

The smallest even square is 2^16 * 5^6 = 1024000000. - Jianing Song, Jun 04 2022

Links

• Jianing Song, Table of n, a(n) for n = 1..10000
• Jianing Song, Possible numbers of divisors of terms in A354715

Crossrefs

Cf. A000005, A033950, A272872, A354711, A354712, A354714, A354716, A354079.

Programs

Mathematica

Select[Range[300], Divisible[# - 2, DivisorSigma[0, #]] &] (* Amiram Eldar, Jun 03 2022 *)

PARI

isA354715(k) = (Mod(k,numdiv(k)) == 2) \\ Jianing Song, Jun 04 2022

Python

from sympy import divisor_count
def ok(n): return n > 0 and (n-2)%divisor_count(n) == 0
print([k for k in range(300) if ok(k)]) # Michael S. Branicky, Jun 04 2022