login
A360327
a(n) is the sum of divisors of n that have only prime-indexed prime factors.
5
1, 1, 4, 1, 6, 4, 1, 1, 13, 6, 12, 4, 1, 1, 24, 1, 18, 13, 1, 6, 4, 12, 1, 4, 31, 1, 40, 1, 1, 24, 32, 1, 48, 18, 6, 13, 1, 1, 4, 6, 42, 4, 1, 12, 78, 1, 1, 4, 1, 31, 72, 1, 1, 40, 72, 1, 4, 1, 60, 24, 1, 32, 13, 1, 6, 48, 68, 18, 4, 6, 1, 13, 1, 1, 124, 1, 12
OFFSET
1,3
COMMENTS
Equivalently, a(n) is the sum of divisors of the largest divisor of n that has only prime-indexed prime factors.
LINKS
FORMULA
a(n) = 1 if and only if n is in A320628.
a(n) = A000203(n) if and only if n is in A076610.
a(n) = A000203(A360325(n)).
Multiplicative with a(p^e) = (p^(e+1)-1)/(p-1) if p is a prime-indexed prime (A006450), and 1 otherwise.
MATHEMATICA
f[p_, e_] := If[PrimeQ[PrimePi[p]], (p^(e+1)-1)/(p-1), 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])), (p[i]^(e[i]+1)-1)/(p[i]-1), 1)); }
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, Feb 03 2023
STATUS
approved