

A180248


Odd composite squarefree numbers k such that r = 2*(p  2 + k/p)/(p1) is an integer for each prime divisor p of k.


1



15, 91, 435, 561, 703, 1105, 1729, 1891, 2465, 2701, 2821, 3367, 5551, 6601, 8695, 8911, 10585, 11305, 12403, 13981, 15051, 15841, 16471, 18721, 23001, 26335, 29341, 30889, 38503, 39865, 41041, 46657, 49141, 52633, 53131, 62745
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OFFSET

1,1


COMMENTS

Conjecture: k is a Carmichael number (A002997) if and only if k is a term of this sequence and all rvalues of k are even.
From Ridouane Oudra, Apr 28 2019: (Start)
This sequence can also be defined as: Odd composite squarefree numbers k such that r' = 2*(k1)/(p1) is an integer for each prime divisor p of k. Proof:
2*(p  2 + k/p)/(p1) + 2*(k/p1) = 2*(k1)/(p1),
so r is an integer if and only if r' is. (2*(k/p1) is always an integer.)
With this new definition and Korselt's theorem it is easily shown that the proposed conjecture is true.
(End)


LINKS

K. Brockhaus, Table of n, a(n) for n = 1..653 (terms < 10^8)


PROG

(PARI) isok(n) = {if (((n % 2)==0)  isprime(n)  !issquarefree(n), return (0)); f = factor(n); for (i=1, #f~, d = f[i, 1]; if (type(2*(d2+n/d)/(d1)) != "t_INT", return(0)); ); return (1); } \\ Michel Marcus, Jul 12 2013


CROSSREFS

Sequence in context: A237516 A020242 A020255 * A041428 A052226 A108684
Adjacent sequences: A180245 A180246 A180247 * A180249 A180250 A180251


KEYWORD

nonn


AUTHOR

William F. Sindelar (w_sindelar(AT)juno.com), Aug 19 2010


EXTENSIONS

Edited by the Associate Editors of the OEIS, Sep 04 2010


STATUS

approved



