A162323 - OEIS

A162323

a(n) = the smallest positive integer such that when a(n) is represented in binary, it contains the binary representations of every prime dividing n as substrings.

1, 2, 3, 2, 5, 6, 7, 2, 3, 5, 11, 6, 13, 14, 11, 2, 17, 6, 19, 5, 7, 11, 23, 6, 5, 13, 3, 14, 29, 11, 31, 2, 11, 17, 23, 6, 37, 19, 13, 5, 41, 14, 43, 11, 11, 23, 47, 6, 7, 5, 35, 13, 53, 6, 11, 14, 19, 29, 59, 11, 61, 62, 7, 2, 13, 11, 67, 17, 23, 23, 71, 6, 73, 37, 11, 19, 23, 13, 79, 5

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OFFSET

1,2

COMMENTS

Contribution from Hagen von Eitzen, Aug 16 2009: (Start)

a(n) = a(A007947(n)). As a consequence one may focus on squarefree n.

Let p be a prime. Then a(p)=p; a(2p) = 2p if p is Mersenne, otherwise a(2p) = p; a(3p) in {p, 2p+1}. (End)

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

35 is factored as 5*7. The binary representations of 5 and 7 are 101 and 111. The smallest positive integer that contains both these binary representations as substrings is 23 (decimal) = 10111 in binary. So a(35) = 23.

CROSSREFS

Sequence in context: A049273 A053590 A208644 * A165743 A086297 A261969

Adjacent sequences: A162320 A162321 A162322 * A162324 A162325 A162326

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Jul 01 2009

EXTENSIONS

More terms from Hagen von Eitzen, Aug 16 2009

STATUS

approved