A162687 - OEIS

A162687

Write the distinct primes dividing n in binary, in order with the largest prime on the left and smallest on the right. Concatenate, and convert to decimal to get a(n).

0, 2, 3, 2, 5, 14, 7, 2, 3, 22, 11, 14, 13, 30, 23, 2, 17, 14, 19, 22, 31, 46, 23, 14, 5, 54, 3, 30, 29, 94, 31, 2, 47, 70, 61, 14, 37, 78, 55, 22, 41, 126, 43, 46, 23, 94, 47, 14, 7, 22, 71, 54, 53, 14, 93, 30, 79, 118, 59, 94, 61, 126, 31, 2, 109, 190, 67, 70, 95, 246, 71, 14, 73, 150, 23, 78, 95, 222, 79, 22, 3, 166, 83, 126, 141, 174, 119, 46, 89, 94, 111, 94, 127, 190, 157, 14, 97, 30, 47, 22

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

OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..20000

EXAMPLE

60 is factored as 5 * 3 * 2^2. Write the distinct prime divisors (largest to smallest) in binary to get 101, 11, 10. Concatenate to get 1011110. a(60) is the decimal equivalent of this, which is 94.

MAPLE

a:= n->(l->add(l[i]*2^(i-1), i=1..nops(l)))(map(j->convert

(j, base, 2)[], sort(map(i-> i[1], ifactors(n)[2])))):

seq(a(n), n=1..100); # Alois P. Heinz, Mar 29 2020

MATHEMATICA

Join[{0}, Table[FromDigits[Flatten[IntegerDigits[Reverse[FactorInteger[n][[All, 1]]], 2]], 2], {n, 2, 100}]] (* Harvey P. Dale, Mar 29 2020 *)

PROG

(PARI) a(n)={if(n==1, 0, fromdigits(concat([digits(k, 2) | k<-Vecrev(factor(n)[, 1])]), 2))} \\ Andrew Howroyd, Mar 29 2020

CROSSREFS

Sequence in context: A345302 A357183 A350177 * A010242 A339645 A318956

Adjacent sequences: A162684 A162685 A162686 * A162688 A162689 A162690

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Jul 10 2009

EXTENSIONS

Extended beyond a(16) by R. J. Mathar, Jul 16 2009

Corrected and extended by Harvey P. Dale, Mar 29 2020

STATUS

approved