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A052331 Inverse of A052330. 4
0, 1, 2, 4, 8, 3, 16, 5, 32, 9, 64, 6, 128, 17, 10, 256, 512, 33, 1024, 12, 18, 65, 2048, 7, 4096, 129, 34, 20, 8192, 11, 16384, 257, 66, 513, 24, 36, 32768, 1025, 130, 13, 65536, 19, 131072, 68, 40, 2049, 262144, 258, 524288, 4097, 514, 132, 1048576, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Every number can be represented uniquely as a product of numbers of the form p^(2^k), sequence A050376. This sequence is a binary representation of this factorization, with a(p^(2^k)) = 2^i, where i is the index of p^(2^k) in A050376. Additive with a(p^e) = sum a(p^(2^e_k)) where e = sum(2^e_k) is the binary representation of e and a(p^(2^k)) is as described above. - Franklin T. Adams-Watters, Oct 25 2005

LINKS

Table of n, a(n) for n=1..54.

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(1)=0; a(n*A050376(k)) = a(n) + 2^k for a(n) < 2^k, k=0, 1, ... - Thomas Ordowski, Mar 23 2005

PROG

(PARI) A052331=a(n)={for(i=1, #n=factor(n)~, n[2, i]>1||next; m=binary(n[2, i]); n=concat(n, Mat(vector(#m-1, j, [n[1, i]^2^(#m-j), m[j]]~))); n[2, i]%=2); n||return(0); m=vecsort(n[1, ]); forprime(p=1, m[#m], my(j=0); while(p^2^j<m[#m], setsearch(m, p^2^j)||n=concat(n, [p^2^j, 0]~); j++)); vector(#n=vecsort(n), i, 2^i)*n[2, ]~>>1} \\ M. F. Hasler, Apr 08 2015

CROSSREFS

Cf. A050376, A052330.

Sequence in context: A277272 A109588 A254788 * A242365 A119436 A277695

Adjacent sequences:  A052328 A052329 A052330 * A052332 A052333 A052334

KEYWORD

nonn

AUTHOR

Christian G. Bower, Dec 15 1999

STATUS

approved

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Last modified November 21 07:11 EST 2017. Contains 294996 sequences.