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A156238 Smallest heptagonal number with n distinct prime factors.

%I A156238 #14 Feb 16 2025 08:33:09
%S A156238 7,18,286,3010,32890,769230,3333330,159189030,16015883940,
%T A156238 477463360374,21643407275490,1148540321999070,18489352726664820,
%U A156238 4561561662153109614,71000485538666794110,14440652550858108745170,927869754030522488795610
%N A156238 Smallest heptagonal number with n distinct prime factors.
%C A156238 a(18) <= 150849873309136386205130310. - _Donovan Johnson_, Feb 15 2012
%H A156238 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Numbers</a>.
%e A156238 a(9) = 16015883940 = 2^2*3^2*5*7*17*19*23*29*59. 16015883940 is the smallest heptagonal number with 9 distinct prime factors.
%o A156238 (Python)
%o A156238 from sympy import primefactors
%o A156238 def A000566(n): return n*(5*n-3)//2
%o A156238 def a(n):
%o A156238     k = 1
%o A156238     while len(primefactors(A000566(k))) != n: k += 1
%o A156238     return A000566(k)
%o A156238 print([a(n) for n in range(1, 9)]) # _Michael S. Branicky_, Jul 18 2021
%o A156238 (Python) # faster version using heptagonal structure
%o A156238 from sympy import primefactors
%o A156238 def A000566(n): return n*(5*n-3)//2
%o A156238 def A000566_distinct_factors(n):
%o A156238     pf1 = primefactors(n)
%o A156238     pf2 = primefactors(5*n-3)
%o A156238     combined = set(pf1) | set(pf2)
%o A156238     return len(combined) if n%4 == 0 or (5*n-3)%4 == 0 else len(combined)-1
%o A156238 def a(n):
%o A156238     k = 1
%o A156238     while A000566_distinct_factors(k) != n: k += 1
%o A156238     return A000566(k)
%o A156238 print([a(n) for n in range(1, 10)]) # _Michael S. Branicky_, Jul 18 2021
%Y A156238 Cf. A000566, A076551, A156236, A156237, A156239.
%K A156238 nonn
%O A156238 1,1
%A A156238 _Donovan Johnson_, Feb 07 2009
%E A156238 a(17) from _Donovan Johnson_, Jul 02 2011