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 A264961 Numbers that are products of two triangular numbers in more than one way. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS One of the factors in the product may be 1 = A000217(1). We count the ways of writing n = A000217(i)*A000217(j) with i <= j, unordered factorizations. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10602 EXAMPLE 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. 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: 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 *) PROG (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 CROSSREFS Subsequence of A085780. A188630 and A110904 are subsequences of this. Sequence in context: A195528 A144291 A068143 * A188630 A167310 A083674 Adjacent sequences:  A264958 A264959 A264960 * A264962 A264963 A264964 KEYWORD nonn AUTHOR R. J. Mathar, Nov 29 2015 STATUS approved

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Last modified January 24 23:49 EST 2021. Contains 340414 sequences. (Running on oeis4.)