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A349379
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Möbius transform of A057521 (powerful part of n).
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2
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1, 0, 0, 3, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 18, 0, 0, 0, 0, 16, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0
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OFFSET
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1,4
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COMMENTS
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Multiplicative with a(p^e) = 0 if e = 1, p^2 - 1 if e = 2 and p^e - p^(e-1) otherwise. - Amiram Eldar, Nov 18 2021
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LINKS
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FORMULA
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MATHEMATICA
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f[p_, e_] := Which[e > 2, p^e - p^(e - 1), e == 2, p^2 - 1, e == 1, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 18 2021 *)
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PROG
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(PARI)
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521
(Python)
from math import prod
from sympy import factorint
def A349379(n): return prod(0 if e==1 else p**e - (1 if e==2 else p**(e-1)) for p, e in factorint(n).items()) # Chai Wah Wu, Nov 14 2022
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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