A273103 Sum of the elements of the difference triangle of the divisors of n (including the divisors of n).

1, 4, 6, 11, 10, 21, 14, 26, 25, 31, 22, 52, 26, 41, 54, 57, 34, 86, 38, 66, 72, 61, 46, 103, 71, 71, 90, 102, 58, 205, 62, 120, 108, 91, 134, 157, 74, 101, 126, 75, 82, 329, 86, 174, 218, 121, 94, 110, 141, 158, 162, 210, 106, 373, 202, 269, 180, 151, 118, -437, 122, 161, 250

Offset: 1

Author

Omar E. Pol, May 15 2016

Keywords

• sign

Comments

a(n) is the sum of the n-th slice of the tetrahedron A273102.

First differs from A187215 at a(14).

Examples

			For n = 14 the divisors of 14 are 1, 2, 7, 14, and the difference triangle of the divisors is
1 . 2 . 7 . 14
. 1 . 5 . 7
. . 4 . 2
. . .-2
The sum of all elements of the triangle is 1 + 2 + 7 + 14 + 1 + 5 + 7 + 4 + 2 - 2 = 41, so a(14) = 41.
Note that A187215(14) = 45.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027750, A125128, A187215, A273102.

Programs

Mathematica

Table[Total@ Flatten@ NestWhileList[Differences, Divisors@ n, Length@ # > 1 &], {n, 63}] (* Michael De Vlieger, May 17 2016 *)

PARI

a(n) = {my(d = divisors(n)); my(s = vecsum(d)); for (k=1, #d-1, d = vector(#d-1, n, d[n+1] - d[n]); s += vecsum(d);); s;} \\ Michel Marcus, May 16 2016

Formula

a(n) = 2n, if n is prime.

a(2^k) = A125128(k+1), k >= 0.

Extensions

More terms from Michel Marcus, May 16 2016