

A190530


Numbers n such that 2^n  3 is not squarefree.


0



7, 16, 27, 47, 67, 87, 88, 107, 124, 127, 139, 147, 162, 167, 187, 198, 207, 227, 247, 267, 272, 280, 287, 303, 307, 308, 314, 327, 341, 347, 367, 387, 407, 415, 418, 427, 436, 447, 467, 481, 485, 487, 507, 514
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OFFSET

1,1


COMMENTS

If for some prime p such that 2^p1 is also prime one has n = 2^(p+1)  3 an odd perfect number, (that is in particular not squarefree), then the even perfect number m = 2^(p1)(2^p1) and the odd perfect number n, are the second pair of perfect numbers (m,n)with m > n such that m/(n+1) is a power of 2. Indeed we have in this case: m/(n+1)=2^(p2). The only other known pair of such numbers is (m,n) = (28,6), so that m/(n+1) = 28/7 = 2^2.


LINKS

Table of n, a(n) for n=1..44.


EXAMPLE

a(7)=88, since 2^88  3 is divisible by 11^2, so that it is not squarefree.


PROG

(PARI) for(n=1, 1000, if(!issquarefree(2^n3), print1(n, ", "))) /* Joerg Arndt, May 13 2011 */


CROSSREFS

Sequence in context: A052221 A119461 A028560 * A133694 A024627 A211784
Adjacent sequences: A190527 A190528 A190529 * A190531 A190532 A190533


KEYWORD

nonn


AUTHOR

Luis H. Gallardo, May 11 2011


EXTENSIONS

a(20)a(44) from Charles R Greathouse IV, May 11, 2011


STATUS

approved



