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A364557
Möbius transform of A005941.
8
1, 1, 2, 2, 4, 2, 8, 4, 4, 4, 16, 4, 32, 8, 4, 8, 64, 4, 128, 8, 8, 16, 256, 8, 8, 32, 8, 16, 512, 4, 1024, 16, 16, 64, 8, 8, 2048, 128, 32, 16, 4096, 8, 8192, 32, 8, 256, 16384, 16, 16, 8, 64, 64, 32768, 8, 16, 32, 128, 512, 65536, 8, 131072, 1024, 16, 32, 32, 16, 262144, 128, 256, 8, 524288, 16, 1048576, 2048
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{d|n} A008683(n/d) * A005941(d).
a(1) = 1; for n > 1, a(n) = A297112(n) = 2^(A297113(n)-1) = 2^A297167(n).
PROG
(PARI) A364557(n) = if(1==n, 1, 2^(primepi(vecmax(factor(n)[, 1]))+(bigomega(n)-omega(n))-1));
(PARI)
A005941(n) = { my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1])-1); res += (p * p2 * (2^(f[i, 2])-1)); p2 <<= f[i, 2]); (1+res) }; \\ (After David A. Corneth's program for A156552)
A364557(n) = sumdiv(n, d, moebius(n/d)*A005941(d));
(Python)
from sympy import factorint, primepi
def A364557(n): return 1<<primepi(max(f:=factorint(n)))+sum(e-1 for e in f.values())-1 if n>1 else 1 # Chai Wah Wu, Jul 29 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 28 2023
STATUS
approved