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A231754 Products of distinct primes congruent to 1 modulo 4 (A002144). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Contains A002144 as a subsequence, and is a subsequence of A016813 and of A005117.

Also, these numbers satisfy A231589(n) = floor(n*(n-1)/4) (A011848).

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..4999

S. A. Shirali, A family portrait of primes-a case study in discrimination, Math. Mag. Vol. 70, No. 4 (Oct., 1997), pp. 263-272.

EXAMPLE

65 = 5*13 is in the sequence since both 5 and 13 are congruent to 1 modulo 4.

MAPLE

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;

end do: # R. J. Mathar, Mar 16 2016

PROG

(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

CROSSREFS

Cf. A002144, A005117, A011848, A016813, A231589.

Sequence in context: A191218 A279857 A077426 * A175768 A002144 A280084

Adjacent sequences:  A231751 A231752 A231753 * A231755 A231756 A231757

KEYWORD

nonn

AUTHOR

Michel Marcus, Nov 13 2013

STATUS

approved

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Last modified April 11 18:59 EDT 2021. Contains 342888 sequences. (Running on oeis4.)