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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If for some prime p such that 2^p-1 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^(p-1)(2^p-1) 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^(p-2). 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^n-3), 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

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Last modified November 18 13:22 EST 2018. Contains 317306 sequences. (Running on oeis4.)