A381060 Numbers t which are the sum of some subset of the values of k satisfying the equation (t - floor((t - k)/k)) mod k = 0 (t > 1, 1 <= k < t).
23, 29, 39, 41, 53, 59, 65, 71, 77, 79, 83, 89, 99, 101, 107, 111, 113, 119, 125, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 199, 209, 221, 227, 233, 239, 245, 251, 257, 263, 269, 279, 281, 287, 293, 299, 305, 311, 317, 323, 329, 335, 339, 341, 349, 353, 359, 365, 371
Offset: 1
Keywords
Examples
23 is in this sequence because the only k's < 23 satisfying the equation (23 - floor((23 - k)/k)) mod k = 0 are: 1, 5, 7, 11, hence: 5+7+11 = 23. 29 is in this sequence because the only k's < 29 satisfying the equation (29 - floor((29 - k)/k)) mod k = 0 are: 1, 2, 3, 5, 9, 14, hence: 1+2+3+9+14 = 29 and 1+5+9+14 = 29. 47 is not in this sequence because the only k's < 47 satisfying the equation (47 - floor((47 - k)/k)) mod k = 0 are: 1, 3, 7, 11, 15, 23 and no subset of these numbers adds to 47.
Programs
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Maxima
(kill(all), s(y):=(f(i,j):=mod(i-floor((i-j)/j),j),s:0,x:1, for k:1 thru floor(y/2) do (if f(y,k)=0 then (s:s+k, B[x]:k, x:x+1)), B:setify(makelist(B[r],r,1,x-1)), s), n:1, for t:2 thru 1000 do (if s(t)>=t then (for b:2 while b<=x-1 and e#t do (C:args(powerset(B,b)), for h:1 while h<=length(C) and e#t do (e:apply("+" , args(C[h])), if e=t then (print(n , " " , t), n:n+1))))));
Comments