OFFSET
1,2
COMMENTS
Every number in this sequence is the product of a unique subset of A225548.
From Peter Munn, Feb 11 2020: (Start)
The terms are the numbers whose Fermi-Dirac factors (see A050376) occur symmetrically about the main diagonal of A329050.
Closed under the commutative binary operation A059897(.,.). As numbers are self-inverse under A059897, the sequence thereby forms a subgroup of the positive integers under A059897.
(End)
LINKS
Paul Tek, Table of n, a(n) for n = 1..10000
EXAMPLE
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
Paul Tek, May 10 2013
STATUS
approved