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 A156238 Smallest heptagonal number with n distinct prime factors. 5
 7, 18, 286, 3010, 32890, 769230, 3333330, 159189030, 16015883940, 477463360374, 21643407275490, 1148540321999070, 18489352726664820, 4561561662153109614, 71000485538666794110, 14440652550858108745170, 927869754030522488795610 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(18) <= 150849873309136386205130310. - Donovan Johnson, Feb 15 2012 LINKS Table of n, a(n) for n=1..17. Eric Weisstein's World of Mathematics, Heptagonal Numbers. EXAMPLE 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. PROG (Python) from sympy import primefactors def A000566(n): return n*(5*n-3)//2 def a(n): k = 1 while len(primefactors(A000566(k))) != n: k += 1 return A000566(k) print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Jul 18 2021 (Python) # faster version using heptagonal structure from sympy import primefactors def A000566(n): return n*(5*n-3)//2 def A000566_distinct_factors(n): pf1 = primefactors(n) pf2 = primefactors(5*n-3) combined = set(pf1) | set(pf2) return len(combined) if n%4 == 0 or (5*n-3)%4 == 0 else len(combined)-1 def a(n): k = 1 while A000566_distinct_factors(k) != n: k += 1 return A000566(k) print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Jul 18 2021 CROSSREFS Cf. A000566, A076551, A156236, A156237, A156239. Sequence in context: A196219 A219772 A219290 * A156295 A350216 A362309 Adjacent sequences: A156235 A156236 A156237 * A156239 A156240 A156241 KEYWORD nonn AUTHOR Donovan Johnson, Feb 07 2009 EXTENSIONS a(17) from Donovan Johnson, Jul 02 2011 STATUS approved

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Last modified May 30 06:59 EDT 2024. Contains 372962 sequences. (Running on oeis4.)