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A065302 Squarefree composite numbers such that the sum of divisor 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 (list; graph; refs; listen; history; text; internal format)
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)) ) } [From Harry J. Smith, Oct 16 2009]

CROSSREFS

Cf. A000203, A008683, A065299-A065303.

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

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Last modified January 22 16:36 EST 2018. Contains 298055 sequences.