OFFSET
1,1
COMMENTS
The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 0, 5, 76, 813, 8080, 81053, 808478, 8097358, 80939928, 809350235, 8094002068, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0809... . - Amiram Eldar, Nov 17 2025
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
EXAMPLE
The sum of the nonunitary divisors of 36 is 2 + 3 + 6 + 12 + 18 = 41.
MATHEMATICA
nusigma[ n_ ] := DivisorSigma[ 1, n ]-Times@@(1+Power@@#&/@FactorInteger[ n ]); For[ n=1, True, n++, If[ nusigma[ n ]>n, Print[ n ] ] ]
PROG
(PARI) usigma(n)= { local(f, s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) }
isok(m) = sigma(m) - usigma(m) > m; \\ Harry J. Smith, Sep 19 2009
(PARI) isok(k) = {my(f = factor(k)); sigma(f) - prod(i = 1, #f~, f[i, 1]^f[i, 2] + 1) > k; } \\ Amiram Eldar, Nov 17 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Dean Hickerson, Sep 25 2001
STATUS
approved