A226111 - OEIS

A226111

Composite squarefree numbers n such that the ratio (n - 1/2)/(p(i) + 1/2) is an integer, where p(i) are the prime factors of n.

260813, 960323, 4572113, 5991098, 18912713, 37481945, 68688458, 214337813, 1418459963, 1488523838, 1905782603, 1906387718, 2416383938, 3866147051, 6153859058, 6927221438, 10696723538, 12000312419, 24529142138, 43004079563, 43648495313, 54750300413

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OFFSET

1,1

COMMENTS

Also composite squarefree numbers n such that (2*p(i)+1) | (2*n-1).

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..62 (terms < 2*10^12)

EXAMPLE

The prime factors of 5991098 are 2, 103, 127 and 229. We see that (5991098 - 1/2)/(2 + 1/2) = 2396439, (5991098 - 1/2)/(103 + 1/2) = 57885, (5991098 - 1/2)/(127 + 1/2) = 46989 and (5991098 - 1/2)/(229 + 1/2) = 26105. Hence 5991098 is in the sequence.

The prime factors of 1123342 are 2, 11 and 51061. We see that(1123342 - 1/2)/(2 + 1/2) = 748895, (1123342 - 1/2)/(11 + 1/2) = 106985 but (1123342 - 1/2)/(51061 + 1/2) = 2246685/102121. Hence 1123342 is not in the sequence.

MAPLE

with(numtheory); A226111:=proc(i, j) local c, d, n, ok, p;

for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;

for d from 1 to nops(p) do if p[d][2]>1 or not type((n-j)/(p[d][1]+j), integer) then ok:=0; break; fi; od;

if ok=1 then print(n); fi; fi; od; end: A226111(10^9, 1/2);

CROSSREFS

Cf. A208728, A225702-A225720, A226020, A226112-A226114.

Sequence in context: A184781 A146897 A249836 * A002272 A172850 A066914

Adjacent sequences: A226108 A226109 A226110 * A226112 A226113 A226114

KEYWORD

nonn,hard

AUTHOR

Paolo P. Lava, May 27 2013

EXTENSIONS

a(8)-a(22) from Giovanni Resta, Jun 02 2013

STATUS

approved