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A353019
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Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2 which are products of five distinct primes.
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0
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32890, 48790, 102718, 167314, 236698, 239785, 260338, 330694, 360430, 389470, 455182, 749938, 884170, 932386, 960070, 1007110, 1104565, 1334806, 1397638, 1423930, 1488802, 1515934, 1610818, 1679770, 1721005, 1741810, 1952314, 2046205, 2312167, 2365363, 2473570, 2503501, 2513518, 2558842
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OFFSET
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1,1
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COMMENTS
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A squarefree subsequence of heptagonal numbers.
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LINKS
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EXAMPLE
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32890 = 2*5*11*13*23 = 115(5*115-3)/2.
48790 = 2*5*7*17*41 = 140(5*140-3)/2.
102718 = 2*7*11*23*29 = 203(5*203-3)/2.
167314 = 2*7*17*19*37 = 259(5*259-3)/2.
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MATHEMATICA
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Select[Table[n*(5*n - 3)/2, {n, 1, 1000}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* Amiram Eldar, Apr 17 2022 *)
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PROG
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(Python)
from sympy import factorint
from itertools import count, islice
def agen():
for h in (n*(5*n-3)//2 for n in count(1)):
f = factorint(h, multiple=True)
if len(f) == len(set(f)) == 5: yield h
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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