A285889 The smaller of the lexicographically least pair (x, y) such that 0 < x < y and sigma(x) = sigma(y) = n + x + y.

220, 48, 174, 390, 102, 280, 160, 500, 66, 132, 54, 24280, 992, 560, 140, 168, 60, 10360, 1120, 1232, 198, 210, 132, 2170, 520, 1520, 96, 168, 330, 732, 60, 4424, 270, 540, 144, 1000, 1484, 4080, 220, 840, 1144, 16500, 1988, 5456, 210, 528, 150, 4158, 1180, 12236

Offset

0,1

Comments

In the first 1000 terms the most repeated number is 840 with 15 occurrences.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Example

a(0) = 220: sigma(220) = sigma(284) = 220 + 284 = 504;
a(1) = 48: sigma(48) = sigma(75) = 48 + 75 + 1 = 124;
a(2) = 174: sigma(174) = sigma(184) = 174 + 184 + 2 = 360.

Maple

with(numtheory): P:=proc(q) local a, b, k, n; for n from 0 to q do for k from 1 to q do
a:=sigma(k)-k-n; b:=sigma(a)-a-n; if a>0 and b=k and a<>b then print(k); break;
fi; od; od; end: P(10^9);

Mathematica

Table[m = 1; While[MissingQ@ Set[k, SelectFirst[Range[m - 1], DivisorSigma[1, m] == DivisorSigma[1, #] == m + # + n &]], m++]; {k, m}, {n, 0, 10}][[All, 1]] (* Version 10.2, or *)
Do[m = 1; While[Set[k, Module[{k = 1}, While[! Xor[DivisorSigma[1, m] == DivisorSigma[1, k] == m + k + n, k >= m], k++]; k]] >= m, m++]; Print@ k, {n, 0, 10}] (* Michael De Vlieger, Apr 28 2017 *)

Prog

(PARI) getfirstterms(n)={my(L:list, S:list, k:small, t); L=List(); S=List([1, 3]); k=0; forstep(i=3, +oo, 1, listput(S, sigma(i)); forvec(j=[[2, i], [2, i]], t=vecsum(j)+k; if((S[j[1]]==t)&&(t==S[j[2]]), listput(L, j[1]); if(k==n, break(2), k++)), 2)); return(Vec(L))} \\ R. J. Cano, May 03 2017

Crossrefs

Cf. A000203, A285890, A285892.

See first terms of A002025 and A005276.

Sequence in context: A166836 A200827 A286441 * A173619 A157645 A157673

Adjacent sequences: A285886 A285887 A285888 * A285890 A285891 A285892

Keyword

nonn,easy

Author

Paolo P. Lava, Apr 28 2017

Status

approved