OFFSET
1,2
COMMENTS
a(n) is the sum of the main divisors of n because n = d_1*d_2*...*d_k*D where d_i are the distinct prime divisors of n and D = n/rad(n).
sopf(n) (A008472) is the sum of the distinct primes dividing n and rad(n) (A007947) is the product of the distinct primes dividing n.
If n is prime, then a(n) = sopf(n) + 1.
LINKS
Michel Lagneau, Table of n, a(n) for n = 1..10000
MAPLE
with(numtheory): a := proc(n) factorset(n):
convert(%, `+`) + n / convert(%, `*`) end:
seq(a(n), n=1..70); # Peter Luschny, Sep 19 2017
MATHEMATICA
rad[n_] := Times@@(First@#&/@FactorInteger@n); sopf[n_] := Plus@@(First@#&/@FactorInteger@n); Rest[Total[Transpose[sopf[#] + #/rad[#]&/@Range[100]]]]
PROG
(PARI) a(n) = my(f=factor(n)[, 1]); vecsum(f) + n/prod(k=1, #f, f[k]); \\ Michel Marcus, Sep 20 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Sep 11 2013
EXTENSIONS
a(1) = 1 prepended by Peter Luschny, Sep 19 2017
STATUS
approved