A094379 Least number having exactly n representations as ab+ac+bc with 1 <= a <= b <= c.

1, 3, 11, 23, 35, 47, 59, 71, 95, 188, 119, 164, 231, 191, 215, 239, 299, 356, 335, 311, 404, 431, 591, 584, 524, 479, 551, 656, 831, 776, 671, 719, 791, 839, 1004, 1031, 959, 1244, 1196, 1439, 1271, 1151, 1931, 1847, 1391, 1319, 1811, 1784, 1616, 1511, 1799

Offset

0,2

Comments

Note that the Mathematica program computes A094379, A094380 and A094381, but outputs only this sequence.

A066955(a(n)) = n and A066955(m) = n for m < a(n). [Reinhard Zumkeller, Mar 23 2012]

References

See A025052

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..125

Example

a(3) = 23 because 23 is the least number with 3 representations: (a,b,c) = (1,1,11), (1,2,7) and (1,3,5).

Mathematica

cntMax=10; nSol=Table[{0, 0, 0}, {cntMax+1}]; Do[lim=Ceiling[(n-1)/2]; cnt=0; Do[If[n>a*b && Mod[n-a*b, a+b]==0 && Quotient[n-a*b, a+b]>=b, cnt++; If[cnt>cntMax, Break[]]], {a, 1, lim}, {b, a, lim}]; If[cnt<=cntMax, If[nSol[[cnt+1, 1]]==0, nSol[[cnt+1, 1]]=n]; nSol[[cnt+1, 2]]=n; nSol[[cnt+1, 3]]++; ], {n, 10000}]; Table[nSol[[i, 1]], {i, cntMax+1}]

Prog

(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a094379 = (+ 1) . fromJust . (`elemIndex` a066955_list)
-- Reinhard Zumkeller, Mar 23 2012

Crossrefs

Cf. A025052 (n having no representations), A093670 (n having one representation), A094380, A094381.

Sequence in context: A100860 A018630 A163780 * A072671 A320901 A119173

Adjacent sequences: A094376 A094377 A094378 * A094380 A094381 A094382

Keyword

nonn

Author

T. D. Noe, Apr 28 2004

Status

approved