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A231754
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Products of distinct primes congruent to 1 modulo 4 (A002144).
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4
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1, 5, 13, 17, 29, 37, 41, 53, 61, 65, 73, 85, 89, 97, 101, 109, 113, 137, 145, 149, 157, 173, 181, 185, 193, 197, 205, 221, 229, 233, 241, 257, 265, 269, 277, 281, 293, 305, 313, 317, 337, 349, 353, 365, 373, 377, 389, 397, 401, 409, 421, 433, 445, 449
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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The number of terms that do not exceed x is ~ c * x / sqrt(log(x)), where c = A088539 * sqrt(A175647) / Pi = 0.3097281805... (Jakimczuk, 2024, Theorem 3.10, p. 26). - Amiram Eldar, Mar 08 2024
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EXAMPLE
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65 = 5*13 is in the sequence since both 5 and 13 are congruent to 1 modulo 4.
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MAPLE
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isA231754 := proc(n)
local d;
for d in ifactors(n)[2] do
if op(2, d) > 1 then
return false;
elif modp(op(1, d), 4) <> 1 then
return false;
end if;
end do:
true ;
end proc:
for n from 1 to 500 do
if isA231754(n) then
printf("%d, ", n) ;
end if;
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MATHEMATICA
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Select[Range[500], # == 1 || AllTrue[FactorInteger[#], Last[#1] == 1 && Mod[First[#1], 4] == 1 &] &] (* Amiram Eldar, Mar 08 2024 *)
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PROG
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(PARI) isok(n) = if (! issquarefree(n), return (0)); if (n > 1, f = factor(n); for (i=1, #f~, if (f[i, 1] % 4 != 1, return (0)))); 1
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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