A226944 Numbers k such that 1/k + Sum_{p|k} 1/p > 1.

30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 462, 480, 510, 540, 546, 570, 600, 630, 660, 690, 714, 720, 750, 780, 798, 810, 840, 858, 870, 900, 924, 930, 960, 966, 990, 1020, 1050, 1080, 1092, 1110, 1140, 1170, 1200, 1218, 1230

Offset: 1

Author

José María Grau Ribas, Jun 23 2013

Keywords

• nonn

Comments

1/k + Sum_{p|k} 1/p = 1 when k is a primary pseudoperfect number (A054377).

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054377.

Programs

Mathematica

fa=FactorInteger; A[n_] := Sum[1/fa[n][[i,1]], {i,Length@fa@n}]; Select[1 + Range@1200, A[#] + 1/# > 1 &]

PARI

is(n)=my(t=1-1/n); forprime(p=2,97,if(n%p==0,n/=p^valuation(n,p);t-=1/p; if(t<0,return(1)))); if(n<101^ceil(101*t), return(0)); my(f=factor(n)[,1]); tCharles R Greathouse IV, Dec 27 2013