

A225547


Fixed points of A225546.


11



1, 2, 9, 12, 18, 24, 80, 108, 160, 216, 625, 720, 960, 1250, 1440, 1792, 1920, 2025, 3584, 4050, 5625, 7500, 8640, 11250, 15000, 16128, 17280, 18225, 21504, 24300, 32256, 36450, 43008, 48600, 50000, 67500, 100000, 135000, 143360, 162000, 193536, 218700, 286720, 321489, 324000, 387072, 437400, 450000, 600000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Every number in this sequence is the product of a unique subset of A225548.
The terms are the numbers whose FermiDirac factors (see A050376) occur symmetrically about the main diagonal of A329050.
Closed under the commutative binary operation A059897(.,.). As numbers are selfinverse under A059897, the sequence thereby forms a subgroup of the positive integers under A059897.
(End)


LINKS



EXAMPLE

The FermiDirac factorization of 160 is 2 * 5 * 16. The factors 2, 5 and 16 are A329050(0,0), A329050(2,0) and A329050(0,2), having symmetry about the main diagonal of A329050. So 160 is in the sequence.


PROG

(PARI) A019565(n) = factorback(vecextract(primes(logint(n+!n, 2)+1), n));
ff(fa) = {for (i=1, #fa~, my(p=fa[i, 1]); fa[i, 1] = A019565(fa[i, 2]); fa[i, 2] = 2^(primepi(p)1); ); fa; } \\ A225546
pos(k, fs) = for (i=1, #fs, if (fs[i] == k, return(i)); );
normalize(f) = {my(list = List()); for (k=1, #f~, my(fk = factor(f[k, 1])); for (j=1, #fk~, listput(list, fk[j, 1])); ); my(fs = Set(list)); my(m = matrix(#fs, 2)); for (i=1, #m~, m[i, 1] = fs[i]; for (k=1, #f~, m[i, 2] += valuation(f[k, 1], fs[i])*f[k, 2]; ); ); m; }
isok(n) = my(fa=factor(n), fb=ff(fa)); normalize(fb) == fa; \\ Michel Marcus, Aug 05 2022


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



