cp's OEIS Frontend

A379965 Numbers k such that (k^2)-1 is not divisible by p^p for any prime p.

%I A379965 #12 Jan 25 2025 02:16:38
%S A379965 2,4,6,8,10,12,14,16,18,20,22,24,30,32,34,36,38,40,42,44,46,48,50,52,
%T A379965 54,56,58,60,62,64,66,68,70,72,74,76,78,84,86,88,90,92,94,96,98,100,
%U A379965 102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,138,140,142,144,146,148,150,152,154,156,158,160
%N A379965 Numbers k such that (k^2)-1 is not divisible by p^p for any prime p.
%C A379965 Numbers k for which (k^2)-1 is in A048103.
%C A379965 Even numbers k such that both k-1 and k+1 are in A048103.
%H A379965 Antti Karttunen, <a href="/A379965/b379965.txt">Table of n, a(n) for n = 1..20000</a>
%o A379965 (PARI) is_A379965 = A379964;
%o A379965 (Python)
%o A379965 from itertools import count, islice
%o A379965 from sympy import factorint
%o A379965 def A379965_gen(startvalue=1): # generator of terms >= startvalue
%o A379965     return filter(lambda n:all(p>e for p,e in factorint(n-1).items()) and all(p>e for p,e in factorint(n+1).items()),count((m:=max(startvalue,1))+(m&1),2))
%o A379965 A379965_list = list(islice(A379965_gen(),30)) # _Chai Wah Wu_, Jan 24 2025
%Y A379965 Cf. A048103, A379964 (characteristic function), A379963.
%Y A379965 Cf. A067874 (subsequence).
%K A379965 nonn
%O A379965 1,1
%A A379965 _Antti Karttunen_, Jan 24 2025