1,1

Comments from Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 18 2006:

"n is in the sequence iff sigma(n)=2n-d(n)+2, where d(n) is number of positive divisors of n. There is no further term up to 105000000.

"If 2^(i+1)+2i-1 is prime then n=2^i*(2^(i+1)+2i-1) is in the sequence because sigma(n)+d(n)-2=(2^(i+1)-1)*(2^(i+1)+2i)+ 2(i+1)-2=2^(2i+2)+2i*2^(i+1)-2^(i+1)=2^(i+1)*(2^(i+1)+2i-1)=2n, so sigma(n)=2n-d(n)+2.

"Hence if i is in {1, 2, 5, 6, 7, 19, 25, 26, 31, 38, 62, 80, 97, 110, 126, 133, 137, 409, 469, 685, 758, 1004, 1025, 1385, 2077, 2646, 2969, 3438, 7806, 8683, ...} then 2^i*(2^(i+1)+2i-1) is in the sequence. 10, 44, 2336, 8896, 34432, 549775212544, 2251801457852416, 9007202677293056, 9223372167851278336, 151115727472444489859072, ... are such terms."

J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172.

f(10) = 11 = 2 + 3 + 6 = f(1) + f(2) + f(5), hence 10 is a term of the sequence.

Select[ Range[ 500000 ], DivisorSigma[ 1, # ] == 2# - DivisorSigma[ 0, # ] + 2 & ] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 18 2006

f[x_] := x + 1; Select[ Range[ 1, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ]

Sequence in context: A122648 A058819 A052394 this_sequence A149226 A155386 A155330

Adjacent sequences: A066226 A066227 A066228 this_sequence A066230 A066231 A066232

nonn

Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 18 2001