OFFSET
1,2
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^(2^floor(log_2(e+1)) - 1).
a(n) = n if and only if n is in A036537.
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 0.7907361848... = Product_{p prime} (1 + Sum_{k>=1} (p^f(k) - p^(f(k-1)+1))/p^(2*k)), f(k) = 2^floor(log_2(k))-1 for k >= 1, and f(0) = 0.
MATHEMATICA
f[p_, e_] := p^(2^Floor[Log2[e + 1]] - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(2^exponent(f[i, 2]+1)-1)); }
(Python)
from math import prod
from sympy import factorint
def A372379(n): return prod(p**((1<<(e+1).bit_length()-1)-1) for p, e in factorint(n).items()) # Chai Wah Wu, Apr 30 2024
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Apr 29 2024
STATUS
approved