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

1, 1, 2, 3, 4, 10, 6, 21, 16, 36, 10, 330, 12, 78, 112, 315, 16, 1360, 18, 2052, 240, 210, 22, 53130, 96, 300, 416, 6318, 28, 146160, 30, 9765, 640, 528, 816, 1570800, 36, 666, 912, 560196, 40, 639600, 42, 27090, 39424, 990, 46, 37456650, 288, 42336, 1600, 45900, 52, 1874080, 2160

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = Product_{k=2..A000005(n)} (A027750(n,k) - 1).

a(p^n) = Product_{k=1..n} (p^k - 1), where p is prime, and n an integer.

a(2^n) = A005329(n).

a(3^n) = A027871(n).

a(5^n) = A027872(n).

a(7^n) = A027875(n).

a(11^n) = A027879(n).

From Amiram Eldar, Nov 02 2024: (Start)

a(n) = n-1 if and only if n is in A175787 (i.e., n = 4 or n is prime).

a(n) == 1 (mod 2) if and only if n is a power of 2 (A000079). (End)

Example

a(12) = (2-1)*(3-1)*(4-1)*(6-1)*(12-1) = 1*2*3*5*11 = 330.

Maple

with(numtheory): seq(mul(d-1, d in divisors(n) minus {1}), n=1..80);

Mathematica

a[n_] := Times @@ (Rest@ Divisors[n] - 1); Array[a, 60] (* Amiram Eldar, Nov 01 2024 *)

Prog

(PARI) a(n) = my(d=divisors(n)); prod(k=2, #d, d[k]-1); \\ Michel Marcus, Oct 30 2024

Crossrefs

Cf. A007955, A020696.

Cf. A000079, A005329, A027871, A027872, A027875, A027879, A175787.

Sequence in context: A334463 A143178 A084190 * A203070 A088303 A193858

Adjacent sequences: A377481 A377482 A377483 * A377485 A377486 A377487

Keyword

nonn,easy

Author

Ridouane Oudra, Oct 29 2024

Status

approved