A109761 Rare pseudoperfect (or semiperfect) numbers, that is, pseudoperfect numbers k such that k == 2 or 10 (mod 12).

350, 490, 550, 650, 770, 910, 1190, 1330, 1430, 1610, 1750, 1870, 2002, 2030, 2090, 2170, 2210, 2450, 2470, 2530, 2590, 2750, 2870, 2990, 3010, 3190, 3230, 3250, 3290, 3410, 3430, 3710, 3770, 3850, 4070, 4130, 4270, 4510, 4550, 4690, 4730, 4970

Offset: 1

Author

Walter Kehowski, Aug 12 2005

Keywords

• nonn

Comments

There are 1232 pseudoperfect numbers less than or equal to 5000 but only 42 rare ones.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..250 from Reinhard Zumkeller)

Crossrefs

Cf. A005835.

Cf. A210455; intersection of A005835 and A091999.

Programs

Haskell

a109761 n = a109761_list !! (n-1)
a109761_list = filter ((== 1) . a210455) a091999_list
-- Reinhard Zumkeller, Jan 21 2013

Maple

with(combinat); issemiperfect := proc(n) local b, S; b:=false; S:=subsets(divisors(n) minus {n}); while not S[finished] do if convert(S[nextvalue](),`+`)=n then b:=true; break fi od; return b end: S:=remove(proc(z) type(z,odd) end,[$1..5000]): SP:=select(proc(z) issemiperfect(z) end, S): RSP:=select(proc(z) z mod 12 = 2 or z mod 12 = 10 end, SP);