|
%I #12 Jun 18 2018 08:40:22
%S 1,26,74,122,146,218,314,362,386,458,554,626,746,794,818,842,866,914,
%T 1082,1202,1226,1322,1346,1418,1466,1514,1538,1658,1706,1754,1874,
%U 1994,2018,2042,2066,2138,2186,2234,2258,2306,2402,2426,2474,2594,2642,2762
%N Squarefree composite numbers whose sum of divisors is also squarefree.
%C 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
%H Harry J. Smith, <a href="/A065302/b065302.txt">Table of n, a(n) for n = 1..1000</a>
%o (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
%Y Cf. A000203, A008683, A065299-A065303.
%Y Cf. A128607, A128608.
%K nonn
%O 1,2
%A _Labos Elemer_, Oct 29 2001
|
