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

1,1

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)

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);

Prog

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

Crossrefs

Cf. A005835.

Cf. A210455; intersection of A005835 and A091999.

Sequence in context: A043619 A249430 A260763 * A109762 A074055 A304282

Adjacent sequences: A109758 A109759 A109760 * A109762 A109763 A109764

Keyword

nonn

Author

Walter Kehowski, Aug 12 2005

Status

approved