A370681 a(n) is the alternating sum of the unitary divisors of n, when these divisors are starting with n and decreasing.

1, 1, 2, 3, 4, 4, 6, 7, 8, 6, 10, 10, 12, 8, 12, 15, 16, 10, 18, 18, 16, 12, 22, 18, 24, 14, 26, 24, 28, 22, 30, 31, 24, 18, 32, 30, 36, 20, 28, 36, 40, 32, 42, 36, 40, 24, 46, 34, 48, 26, 36, 42, 52, 28, 48, 54, 40, 30, 58, 46, 60, 32, 60, 63, 56, 48, 66, 54

Offset

1,3

Comments

a(n) is odd if and only if n is a power of 2.

Links

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

Formula

a(n) = A071324(n) if n is squarefree (A005117) or if n is in A370683.

Example

The unitary divisors of 6 are {1, 2, 3, 6}, hence a(6) = 6 - 3 + 2 - 1 = 4.
The unitary divisors of 12 are {1, 3, 4, 12}, hence a(12) = 12 - 4 + 3 - 1 = 10.

Mathematica

a[n_] := Module[{d = Reverse[Select[Divisors[n], CoprimeQ[#, n/#] &]]}, Total[(-1)^(Range[Length[d]] + 1)*d]]; Array[a, 100]

Prog

(PARI) a(n) = {my(d = Vecrev(select(x->(gcd(x, n/x) == 1), divisors(n)))); sum(i=1, #d, (-1)^(i+1)*d[i]); }

Crossrefs

Cf. A005117, A034448, A071323, A071324, A077610, A370683.

Sequence in context: A205791 A039696 A076332 * A245092 A342126 A092601

Adjacent sequences: A370678 A370679 A370680 * A370682 A370683 A370684

Keyword

nonn,easy

Author

Amiram Eldar, Feb 26 2024

Status

approved