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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A227371 A117847 A057990 * A173477 A091022 A133372

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

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Last modified September 29 06:29 EDT 2020. Contains 337425 sequences. (Running on oeis4.)