A264961 Numbers that are products of two triangular numbers in more than one way.
36, 45, 210, 315, 360, 630, 780, 990, 1260, 1386, 1540, 1800, 2850, 2970, 3510, 3570, 3780, 4095, 4788, 4851, 6300, 7920, 8415, 8550, 8778, 9450, 11700, 11781, 14850, 15400, 15561, 16380, 17640, 17955, 18018, 18648, 19110, 20790, 21420, 21450, 21528, 25116, 25200, 26565, 26775, 26796, 27720, 28980
Offset: 1
Keywords
Examples
36 = 1*36 = 6*6. 45 = 1*45 = 3*15. 210 = 1*210 = 10*21. 315 = 3*105 = 15*21. 360 = 3*120 = 10*36. 630 = 1*630 = 3*210 = 6*105. 3780= 6*360 = 10 * 378 = 36*105.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10602
Programs
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Maple
A264961ct := proc(n) local ct,d ; ct := 0 ; for d in numtheory[divisors](n) do if d^2 > n then return ct; end if; if isA000217(d) then if isA000217(n/d) then ct := ct+1 ; end if; end if; end do: return ct; end proc: for n from 1 to 30000 do if A264961ct(n) > 1 then printf("%d,",n) ; end if; end do:
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Mathematica
lim = 10000; t = Accumulate[Range@lim]; f[n_] := Select[{#, n/#} & /@ Select[Divisors@ n, # <= Sqrt@ n && MemberQ[t, #] &], MemberQ[t, Last@ #] &]; Select[Range@ lim, Length@ f@ # == 2 &] (* Michael De Vlieger, Nov 29 2015 *) -
Python
from _future_ import division mmax = 10**3 tmax, A264961_dict = mmax*(mmax+1)//2, {} ti = 0 for i in range(1,mmax+1): ti += i p = ti*i*(i-1)//2 for j in range(i,mmax+1): p += ti*j if p <= tmax: A264961_dict[p] = 2 if p in A264961_dict else 1 else: break A264961_list = sorted([i for i in A264961_dict if A264961_dict[i] > 1]) # Chai Wah Wu, Nov 29 2015
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