

A065302


Squarefree composite numbers whose sum of divisors is also squarefree.


2



1, 26, 74, 122, 146, 218, 314, 362, 386, 458, 554, 626, 746, 794, 818, 842, 866, 914, 1082, 1202, 1226, 1322, 1346, 1418, 1466, 1514, 1538, 1658, 1706, 1754, 1874, 1994, 2018, 2042, 2066, 2138, 2186, 2234, 2258, 2306, 2402, 2426, 2474, 2594, 2642, 2762
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OFFSET

1,2


COMMENTS

All elements except the first, a(1)=1, are of the form 2*p, where p is a prime and p == 1 (mod 12). Also, sigma(2*p) = (1+2)*(1+p) = 6m where m = (1+p)/2 and m == 1 (mod 6). A squarefree composite number not of the form 2*p cannot be in the sequence since sigma is multiplicative. For example, sigma(p*q) = (1+p)*(1+q) is divisible by 4 for p,q > 2.  Walter Kehowski, Mar 21 2007


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000


PROG

(PARI) { n=0; for (m = 1, 10^9, if (!isprime(m) && moebius(m) && moebius(sigma(m)), write("b065302.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 16 2009


CROSSREFS

Cf. A000203, A008683, A065299A065303.
Cf. A128607, A128608.
Sequence in context: A039377 A043200 A043980 * A044164 A044545 A255185
Adjacent sequences: A065299 A065300 A065301 * A065303 A065304 A065305


KEYWORD

nonn


AUTHOR

Labos Elemer, Oct 29 2001


STATUS

approved



