A364557 - OEIS

A364557

Möbius transform of A005941.

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

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OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

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

Cf. A005941, A008683, A297112, A297113, A297167, A364558.

Sequence in context: A200147 A235063 A084540 * A297112 A259192 A307313

Adjacent sequences: A364554 A364555 A364556 * A364558 A364559 A364560

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 28 2023

STATUS

approved