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A273103
Sum of the elements of the difference triangle of the divisors of n (including the divisors of n).
14
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
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
KEYWORD
sign
AUTHOR
Omar E. Pol, May 15 2016
EXTENSIONS
More terms from Michel Marcus, May 16 2016
STATUS
approved