A227270 Numbers m 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 m.

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

Author

Michel Lagneau, Jul 04 2013

Keywords

• nonn
• easy

Examples

			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.
		

Links

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

Crossrefs

Cf A069819.

Programs

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 *)