A280515 Amicable pairs where only abundant aliquot parts are considered.

288, 450, 2640, 5778, 379632, 588042, 1658640, 3041514, 2907680, 3743440, 4235160, 7165314, 4612080, 10113066, 24103980, 40475214, 25858020, 33363990, 51447792, 80640522, 76202040, 130466754, 76286064, 100954890, 79343220, 106451334, 110175060, 143633574, 155611632

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Example

Abundant aliquot parts of 288 are 12, 18, 24, 36, 48, 72, 96, 144 and their sum is 450.
Abundant aliquot parts of 450 are 18, 30, 90, 150 and their sum is 288.

Maple

with(numtheory): P:=proc(q) local a, b, c, d, k, n; for n from 1 to q do
a:=sort([op(divisors(n))]);  b:=0; for k from 1 to nops(a)-1 do if 2*a[k]<sigma(a[k]) then b:=b+a[k]; fi; od;
c:=sort([op(divisors(b))]); d:=0; for k from 1 to nops(c)-1 do if 2*c[k]<sigma(c[k]) then d:=d+c[k]; fi; od; if d=n and d<>b then print(n); fi; od; end: P(10^6);

Mathematica

abQ[n_] := DivisorSigma[1, n] > 2n; s[n_] := DivisorSum[n, #&, #<n && abQ[#]&]; seq={}; Do[m=s[n]; If[m>n && s[m]==n, AppendTo[seq, {n, m}]], {n, 1, 10^5}]; Flatten[seq] (* Amiram Eldar, Jan 26 2019 *)

Crossrefs

Cf. A063990, A259180, A280516.

Sequence in context: A345553 A345807 A244196 * A061831 A250774 A082994

Adjacent sequences: A280512 A280513 A280514 * A280516 A280517 A280518

Keyword

nonn,tabf

Author

Paolo P. Lava, Jan 04 2017

Extensions

Data corrected and extended by Amiram Eldar, Jan 26 2019

Status

approved