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

1,2

Comments

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

First differs from A187215 at a(14).

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A027750, A125128, A187215, A273102.

Sequence in context: A132149 A129235 A012903 * A187215 A365647 A322577

Adjacent sequences: A273100 A273101 A273102 * A273104 A273105 A273106

Keyword

sign

Author

Omar E. Pol, May 15 2016

Extensions

More terms from Michel Marcus, May 16 2016

Status

approved