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A377484 a(n) = Product_{d|n, d>1} (d - 1).

%I A377484 #27 Nov 02 2024 09:14:21
%S A377484 1,1,2,3,4,10,6,21,16,36,10,330,12,78,112,315,16,1360,18,2052,240,210,
%T A377484 22,53130,96,300,416,6318,28,146160,30,9765,640,528,816,1570800,36,
%U A377484 666,912,560196,40,639600,42,27090,39424,990,46,37456650,288,42336,1600,45900,52,1874080,2160
%N A377484 a(n) = Product_{d|n, d>1} (d - 1).
%H A377484 Amiram Eldar, <a href="/A377484/b377484.txt">Table of n, a(n) for n = 1..10000</a>
%F A377484 a(n) = Product_{k=2..A000005(n)} (A027750(n,k) - 1).
%F A377484 a(p^n) = Product_{k=1..n} (p^k - 1), where p is prime, and n an integer.
%F A377484 a(2^n) = A005329(n).
%F A377484 a(3^n) = A027871(n).
%F A377484 a(5^n) = A027872(n).
%F A377484 a(7^n) = A027875(n).
%F A377484 a(11^n) = A027879(n).
%F A377484 From _Amiram Eldar_, Nov 02 2024: (Start)
%F A377484 a(n) = n-1 if and only if n is in A175787 (i.e., n = 4 or n is prime).
%F A377484 a(n) == 1 (mod 2) if and only if n is a power of 2 (A000079). (End)
%e A377484 a(12) = (2-1)*(3-1)*(4-1)*(6-1)*(12-1) = 1*2*3*5*11 = 330.
%p A377484 with(numtheory): seq(mul(d-1, d in divisors(n) minus {1}), n=1..80);
%t A377484 a[n_] := Times @@ (Rest@ Divisors[n] - 1); Array[a, 60] (* _Amiram Eldar_, Nov 01 2024 *)
%o A377484 (PARI) a(n) = my(d=divisors(n)); prod(k=2, #d, d[k]-1); \\ _Michel Marcus_, Oct 30 2024
%Y A377484 Cf. A007955, A020696.
%Y A377484 Cf. A000079, A005329, A027871, A027872, A027875, A027879, A175787.
%K A377484 nonn,easy
%O A377484 1,3
%A A377484 _Ridouane Oudra_, Oct 29 2024