A386302 Positive integers k such that the set {d+k/d : d|k} contains three consecutive integers.
144, 180, 1260, 1440, 2520, 5040, 5544, 7200, 14040, 15120, 25200, 31680, 33660, 37800, 46800, 59400, 62244, 65520, 70560, 83160, 107100, 110880, 115920, 166320, 169344, 176400, 180180, 183600, 190944, 221760, 277200, 287280, 297540
Offset: 1
Keywords
Examples
a(1)=144, since 144/12+12=24, 144/9+9=25, 144/8+8=26, and no smaller integer with such property exists.
Links
- Giedrius Alkauskas, Consecutive integers in the set S_n={d+n/d: d|n}
Programs
-
Maple
M:=300000: Ki:={}: Vi:=floor(sqrt(2*M)): Ski:=floor((19*M)^(1/4)/2): for F from 1 to Vi-4 do for y from 1 to min(floor((Vi-F)/2),Ski) do G:=F+2*y+1: if issqr(2*F^2-G^2+2) then x:=(F+G-1)/2; n:=x*(x+1)*y*(y+1): Ki:=Ki union {n}: end if: end do: end do: Ki; -
PARI
isok(m, nb=3) = nb--; my(v = Set(apply(x->x+m/x, divisors(m)))); if (#v >= nb, select(x->(x==nb), vector(#v-nb, k, v[k+nb]-v[k]))); \\ Michel Marcus, Jul 18 2025
Comments