cp's OEIS Frontend

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

%I A354715 #22 Jun 05 2022 10:50:26
%S A354715 1,2,6,10,14,20,22,26,32,34,38,42,44,46,50,58,62,66,68,74,82,86,92,94,
%T A354715 98,106,112,114,116,118,122,130,134,138,142,146,154,158,162,164,166,
%U A354715 170,178,186,188,194,202,206,210,212,214,218,226,236,242,250,254,258,262,266,272,274,278,282
%N A354715 Numbers k such that the number of divisors of k divides k-2.
%C A354715 Numbers k such that k == 2 (mod A000005(k)).
%C A354715 Odd terms are squares. Next odd term after 1 is 5^16 * 29^6 = 90762835845947265625 (cf. A354716).
%C A354715 The smallest even square is 2^16 * 5^6 = 1024000000. - _Jianing Song_, Jun 04 2022
%H A354715 Jianing Song, <a href="/A354715/b354715.txt">Table of n, a(n) for n = 1..10000</a>
%H A354715 Jianing Song, <a href="/A354715/a354715.pdf">Possible numbers of divisors of terms in A354715</a>
%t A354715 Select[Range[300], Divisible[# - 2, DivisorSigma[0, #]] &] (* _Amiram Eldar_, Jun 03 2022 *)
%o A354715 (PARI) isA354715(k) = (Mod(k,numdiv(k)) == 2) \\ _Jianing Song_, Jun 04 2022
%o A354715 (Python)
%o A354715 from sympy import divisor_count
%o A354715 def ok(n): return n > 0 and (n-2)%divisor_count(n) == 0
%o A354715 print([k for k in range(300) if ok(k)]) # _Michael S. Branicky_, Jun 04 2022
%Y A354715 Cf. A000005, A033950, A272872, A354711, A354712, A354714, A354716, A354079.
%K A354715 nonn
%O A354715 1,2
%A A354715 _Max Alekseyev_, Jun 03 2022