OFFSET
1,2
COMMENTS
Equivalently, a(n) is the sum of divisors of the largest divisor of n that has only prime factors that are not prime-indexed primes.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
MAPLE
a:= n-> mul(`if`(isprime(numtheory[pi](i[1])), 1,
(i[1]^(i[2]+1)-1)/(i[1]-1)), i=ifactors(n)[2]):
seq(a(n), n=1..75); # Alois P. Heinz, Feb 03 2023
MATHEMATICA
f[p_, e_] := If[PrimeQ[PrimePi[p]], 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(isprime(primepi(p[i])), 1, (p[i]^(e[i]+1)-1)/(p[i]-1))); }
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, Feb 03 2023
STATUS
approved