OFFSET
1,2
COMMENTS
Antiharmonic numbers (A020487) which are not the product of an antiharmonic number and a relatively prime square > 1. Apart from the first term, a subsequence of A227771 (antiharmonic numbers that are not squares).
Is this sequence infinite? It seems that 4n^2 <= a(n) <= 8n^2 for n > 1, and that a(n) ~ 6n^2 as n -> infinity--see A228036 for motivation.
The antiharmonic mean of the divisors of a(n) is A228024(n).
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
200 = 2^3 * 5^2 is antiharmonic (since sigma_2(200)/sigma(200) = 119 is an integer) but 2^3 is not antiharmonic, so 200 is in this sequence.
180 = 2^2 * 3^2 * 5 is antiharmonic but 180/3^2 = 20 is also antiharmonic, so 180 is not in the sequence.
PROG
(PARI) isf(f)=denominator(prod(i=1, #f~, (f[i, 1]^(f[i, 2]+1)+1)/(f[i, 1]+1)))==1
nosmaller(f, startAt)=for(i=startAt, #f~, if(f[i, 2]%2==0&&f[i, 2], return(nosmaller(f, i+1)&&!(f[i, 2]=0)&&!isf(f)&&nosmaller(f, i+1)))); 1
is(n)=my(f); isf(f=factor(n))&&nosmaller(f, 1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Charles R Greathouse IV and Jonathan Sondow, Aug 03 2013
STATUS
approved