OFFSET
1,1
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
Semiperfect primes p as sums of divisors of p + 1, cf. A390728.
5 = 2 + 3;
11 = 2 + 3 + 6;
17 = 2 + 6 + 9;
19 = 4 + 5 + 10;
23 = 2 + 3 + 4 + 6 + 8;
29 = 3 + 5 + 6 + 15;
41 = 6 + 14 + 21;
47 = 2 + 3 + 4 + 6 + 8 + 24;
47 = 2 + 3 + 6 + 8 + 12 + 16;
53 = 2 + 6 + 18 + 27;
59 = 2 + 3 + 4 + 5 + 10 + 15 + 20;
71 = 2 + 3 + 4 + 6 + 8 + 12 + 36;
79 = 2 + 4 + 5 + 8 + 20 + 40;
83 = 2 + 3 + 4 + 6 + 7 + 12 + 21 + 28;
89 = 2 + 3 + 5 + 6 + 10 + 15 + 18 + 30;
MAPLE
issum:= proc(n, S) option remember; local m, Sp;
Sp:= select(`<=`, S, n);
if n > convert(Sp, `+`) then return false fi;
if member(n, Sp) then return true fi;
m:= max(Sp); Sp:= Sp minus {m};
procname(n-m, Sp) or procname(n, Sp)
end proc:
filter:= proc(n)
local S;
S:= numtheory:-divisors(n+1) minus {n+1};
issum(n, S) and issum(n+1, S)
end proc:
select(filter, [seq(ithprime(i), i=1..200)]); # Robert Israel, Nov 26 2025
MATHEMATICA
pseudoPerfectQ[k_] := Module[{divs = Most[Divisors[k]]}, MemberQ[Total/@Subsets[ divs, Length[ divs]], k]]; pp2Q[k_]:= Module[{divs = Most[Divisors[k+1]]}, MemberQ[Total/@Subsets[ divs, Length[ divs]], k]]; Select[Prime[Range[70]], pseudoPerfectQ[#+1]&&pp2Q[#]&] (* James C. McMahon, Nov 26 2025 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 25 2025
STATUS
approved
