OFFSET
1,8
COMMENTS
If e > 0 is the exponent of the highest power of p dividing n (where p is a prime), then for each divisor d of n that is both an infinitary and an exponential divisor, the exponent of the highest power of p dividing d is a number k such that k | e and the bitwise AND of e and k is equal to k.
The least term that is higher than 2 is a(216) = 4.
LINKS
FORMULA
EXAMPLE
a(8) = 2 since 8 has 2 divisors that are both infinitary and exponential: 2 and 8.
MATHEMATICA
s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; f[p_, e_] := s[e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) s(n) = sumdiv(n, d, bitand(d, n)==d);
a(n) = {my(f = factor(n)); prod(i = 1, #f~, s(f[i, 2])); }
(Python)
from math import prod
from sympy import divisors, factorint
def A359411(n): return prod(sum(1 for d in divisors(e, generator=True) if e|d == e) for e in factorint(n).values()) # Chai Wah Wu, Sep 01 2023
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, Dec 30 2022
STATUS
approved