A378054 - OEIS

A378054

Numbers k that divide A378053(k) = gcd(Product_{d|k} (d + 1), Product_{d|k, d>1} (d - 1)).

%I #8 Nov 15 2024 11:17:29

%S 1,60,90,120,144,168,180,210,240,252,280,336,360,420,504,540,560,630,

%T 660,720,840,900,924,990,1008,1056,1080,1092,1200,1260,1320,1404,1440,

%U 1512,1560,1680,1800,1848,1872,1890,1980,2016,2100,2112,2160,2184,2310,2376,2400

%N Numbers k that divide A378053(k) = gcd(Product_{d|k} (d + 1), Product_{d|k, d>1} (d - 1)).

%C After the first term a(1) = 1, the next odd term is a(71) = 3465, the next term that is coprime to 6 is a(1058) = 95095, and the next term that is coprime to 30 is a(12174) = 2263261.

%H Amiram Eldar, <a href="/A378054/b378054.txt">Table of n, a(n) for n = 1..10000</a>

%e 60 is a term since A378053(60) = 166320 = 60 * 2772 is divisible by 60.

%t Select[Range[2500], And @@ Divisible[{Times @@ ((d = Divisors[#]) + 1), Times @@ (Rest @ d - 1)}, #] &]

%o (PARI) is(k) = if(k == 1, 1, my(d = divisors(k)); !(gcd(prod(k=1, #d, d[k]+1), prod(k=2, #d, d[k]-1)) % k));

%Y Intersection of A056954 and A355331.

%Y A378055 is a subsequence.

%Y Cf. A020696, A377484, A378053, A378058.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 15 2024