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A140394
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Numbers n, satisfying A055231(n+1)- A055231(n)=1, and with n and n+1 not squarefree.
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0
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49, 1681, 18490, 23762, 39325, 57121, 182182, 453962, 656914, 843637, 1431125, 1608574, 1609674, 1940449, 2328482, 2948406, 3203050, 3721549, 5606230, 6352825, 8984002, 10000165, 13502254
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| There exists an infinity numbers divisible by a square and satisfying A055231(n+1) - A055231(n) = 1 because the Fermat-Pell equation 2x^2 - y^2 = 1 admits an infinity of solutions.
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REFERENCES
| J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 49, p. 18, Ellipses, Paris 2008.
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EXAMPLE
| 49 is in the sequence because A055231(50) - A055231(49) = A055231(2*5^2) - A055231(7^2) = 2 - 1 = 1;
18490 is in the sequence because A055231(18491) - A055231(18490) = A055231(11*41^2) -A055231(2*5*43^2) = 11 - 10 = 1.
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MAPLE
| A055231 := proc(n)
a := 1 ;
if n > 1 then
for f in ifactors(n)[2] do
if op(2, f) = 1 then
a := a*op(1, f) ;
end if;
end do:
end if;
a ;
end proc:
isA013929 := proc(n)
n>3 and not numtheory[issqrfree](n) ;
end proc:
isA140394 := proc(n)
isA013929(n) and isA013929(n+1) and (A055231(n+1) -A055231(n) = 1) ;
end proc:
for n from 1 do
if isA140394(n) then
print(n);
end if;
end do: # R. J. Mathar, Dec 23 2011
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CROSSREFS
| Cf. A055231, A007913, A068781.
Sequence in context: A203500 A069327 A088068 * A008843 A145848 A014942
Adjacent sequences: A140391 A140392 A140393 * A140395 A140396 A140397
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KEYWORD
| nonn
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AUTHOR
| Michel Lagneau (mn.lagneau2(AT)orange.fr), Dec 19 2011
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