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

%I A273103 #15 May 17 2016 14:25:51
%S A273103 1,4,6,11,10,21,14,26,25,31,22,52,26,41,54,57,34,86,38,66,72,61,46,
%T A273103 103,71,71,90,102,58,205,62,120,108,91,134,157,74,101,126,75,82,329,
%U A273103 86,174,218,121,94,110,141,158,162,210,106,373,202,269,180,151,118,-437,122,161,250
%N A273103 Sum of the elements of the difference triangle of the divisors of n (including the divisors of n).
%C A273103 a(n) is the sum of the n-th slice of the tetrahedron A273102.
%C A273103 First differs from A187215 at a(14).
%H A273103 Michael De Vlieger, <a href="/A273103/b273103.txt">Table of n, a(n) for n = 1..10000</a>
%F A273103 a(n) = 2n, if n is prime.
%F A273103 a(2^k) = A125128(k+1), k >= 0.
%e A273103 For n = 14 the divisors of 14 are 1, 2, 7, 14, and the difference triangle of the divisors is
%e A273103 1 . 2 . 7 . 14
%e A273103 . 1 . 5 . 7
%e A273103 . . 4 . 2
%e A273103 . . .-2
%e A273103 The sum of all elements of the triangle is 1 + 2 + 7 + 14 + 1 + 5 + 7 + 4 + 2 - 2 = 41, so a(14) = 41.
%e A273103 Note that A187215(14) = 45.
%t A273103 Table[Total@ Flatten@ NestWhileList[Differences, Divisors@ n, Length@ # > 1 &], {n, 63}] (* _Michael De Vlieger_, May 17 2016 *)
%o A273103 (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
%Y A273103 Cf. A027750, A125128, A187215, A273102.
%K A273103 sign
%O A273103 1,2
%A A273103 _Omar E. Pol_, May 15 2016
%E A273103 More terms from _Michel Marcus_, May 16 2016