A227270 Numbers n such that Sum_{i= 1..k} 1/d(i) + Product_{i= 1..k} 1/d(i) = 1, where d(i) are the k prime distinct divisors of n.

1, 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 42, 48, 54, 64, 72, 84, 96, 108, 126, 128, 144, 162, 168, 192, 216, 252, 256, 288, 294, 324, 336, 378, 384, 432, 486, 504, 512, 576, 588, 648, 672, 756, 768, 864, 882, 972, 1008, 1024, 1134, 1152, 1176, 1296, 1344, 1458

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Example

42 is in the sequence because the prime divisors of 42 are 2, 3, 7 and 1/2 + 1/3 + 1/7 + 1/(2*3*7) = 1.

Maple

with(numtheory):for n from 1 to 5000 do: x:=factorset(n):n1:=nops(x): d:= sum('1/x[i] ', 'i'=1..n1) + product('1/x[j] ', 'j'=1..n1):if d=1  then printf(`%d, `, n):else fi:od:

Mathematica

pdd1Q[n_]:=Module[{c=FactorInteger[n][[All, 1]]}, Total[1/c]+ 1/Times@@c ==1]; Join[{1}, Select[Range[1500], pdd1Q]] (* Harvey P. Dale, Aug 22 2016 *)

Crossrefs

Cf A069819.

Sequence in context: A140067 A364157 A067946 * A145853 A318782 A064527

Adjacent sequences: A227267 A227268 A227269 * A227271 A227272 A227273

Keyword

nonn,easy

Author

Michel Lagneau, Jul 04 2013

Status

approved