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a(n) is the smallest number k such that k*n is a term of A072873.
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%I #13 Feb 15 2024 15:32:30

%S 1,2,9,1,625,18,117649,2,3,1250,25937424601,9,23298085122481,235298,

%T 5625,1,48661191875666868481,6,104127350297911241532841,625,1058841,

%U 51874849202,907846434775996175406740561329,18,125,46596170244962,1,117649,88540901833145211536614766025207452637361

%N a(n) is the smallest number k such that k*n is a term of A072873.

%H Amiram Eldar, <a href="/A365637/b365637.txt">Table of n, a(n) for n = 1..388</a>

%F Multiplicative with a(p^e) = p^(p*ceiling(e/p) - e).

%F a(n) = A365636(n)/n.

%F a(n) >= 1 with equality if and only if n is in A072873.

%t f[p_, e_] := p^(Ceiling[e/p]*p - e); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30]

%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^(f[i,1] * ceil(f[i,2] / f[i,1]) - f[i,2]));}

%Y Cf. A072873, A365636.

%K nonn,easy,mult

%O 1,2

%A _Amiram Eldar_, Sep 14 2023

%E Data, formulas and codes corrected by _Amiram Eldar_, Feb 15 2024