A272779 Numbers n such that n*(n+1)/2 - sigma(n) = concat(s,t) and n = s + t, where sigma(n) is the sum of the divisors of n.

10, 15, 24, 136, 196, 1266, 5217, 8236, 8695, 46338, 98826, 181000, 387145, 705250, 1226175, 1291122, 3809269, 8778718, 9294985, 37478179, 49945002, 63158635, 159342696, 175624512, 419753094, 4606837030, 4939169059, 10229566834

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Example

10*11/2 - sigma(10) = 55 - 18 = 37 and 3 + 7 = 10;
5217*5218/2 - sigma(5217) = 13611153 - 7296 = 13603857 and 1360 + 3857 = 5217.

Maple

with(numtheory): P:=proc(q) local a, b, c, i, n;
for n from 1 to q do c:=n*(n+1)/2-sigma(n); for i from 1 to ilog10(c) do
a:=trunc(c/10^i);  b:=c-a*10^i; if a+b=n then print(n); break;
fi; od; od; end: P(10^9);

Mathematica

Select[Range[10^5], Function[n, Total@ Boole@ Function[k, n == First@ # + Last@ # & /@ Map[FromDigits /@ TakeDrop[IntegerDigits@ k, #] &, Range[IntegerLength@ k - 1]]][n (n + 1)/2 - DivisorSigma[1, n]] > 0]] (* Michael De Vlieger, May 07 2016, Version 10.2 *)
ok[t_, n_] := Catch@ Block[{p=10}, While[p<t, If[n == Mod[t, p] + Floor[t/p], Throw@ True, p *= 10]]; False]; Select[ Range[10^5], ok[# (# + 1)/2 - DivisorSigma[1, #], #] &] (* Giovanni Resta, May 07 2016, older Mma, faster *)

Crossrefs

Cf. A000203, A024816, A272778.

Sequence in context: A171444 A227371 A057990 * A173477 A091022 A340731

Adjacent sequences: A272776 A272777 A272778 * A272780 A272781 A272782

Keyword

nonn,base

Author

Paolo P. Lava, May 06 2016

Extensions

a(15)-a(28) from Giovanni Resta, May 07 2016

Status

approved