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
Examples
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.
Links
- Paolo P. Lava, Table of n, a(n) for n = 0..1000
Programs
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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);
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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 *) -
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
Comments