A300794 Least number k that is expressible as the sum of 2 abundant numbers in n ways.

24, 36, 48, 66, 60, 84, 90, 96, 108, 126, 120, 150, 144, 174, 168, 364, 180, 234, 392, 228, 216, 252, 240, 294, 264, 288, 330, 342, 312, 300, 336, 402, 390, 372, 700, 396, 360, 450, 408, 432, 848, 522, 456, 492, 420, 558, 546, 516, 594, 504, 480, 552, 642, 540

Offset: 1

Author

Paolo P. Lava, Mar 13 2018

Keywords

• nonn
• easy

Examples

			a(1) = 24 = 12 + 12;
a(2) = 36 = 12 + 24 = 18 + 18;
a(3) = 48 = 12 + 36 = 18 + 30 = 24 + 24;
a(4) = 66 = 12 + 54 = 18 + 48 = 24 + 42 = 30 + 36,
etc.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005101.

Programs

Maple

with(numtheory); P:=proc(q) local a, b, i, j, n, v; v:=array(1..10^4);
for n from 1 to 10^4 do v[n]:=0; od; a:=0;
for n from 1 to q do b:=0; for i from 1 to trunc(n/2) do
if sigma(i)>2*i and sigma(n-i)>2*(n-i) then b:=b+1; fi; od;
if b=a+1 then a:=b; print(n); j:=1;
while v[b+j]>0 do a:=b+j; print(v[b+j]); j:=j+1; od; else if b>a+1 then
if v[b]=0 then v[b]:=n; fi; fi; fi; od; end: P(10^6);

Mathematica

a[n_] := Block[{t=0, lim=0, ab={}}, While[t == 0, ab = Join[ab, Select[ Range[lim, lim + 499], DivisorSigma[1, #] > 2 # &]]; t = SelectFirst[ Range[lim, lim + 499], Length[ IntegerPartitions[#, {2}, ab]] == n &, 0]; lim += 500]; t]; Array[a, 54] (* Giovanni Resta, Mar 14 2018 *)