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 A365636 a(n) is the smallest multiple of n that is a term of A072873. 2

%I #15 Feb 16 2024 05:27:26

%S 1,4,27,4,3125,108,823543,16,27,12500,285311670611,108,

%T 302875106592253,3294172,84375,16,827240261886336764177,108,

%U 1978419655660313589123979,12500,22235661,1141246682444,20880467999847912034355032910567,432,3125,1211500426369012,27,3294172

%N a(n) is the smallest multiple of n that is a term of A072873.

%H Amiram Eldar, <a href="/A365636/b365636.txt">Table of n, a(n) for n = 1..388</a>

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

%F a(n) = n * A365637(n).

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

%F Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p/(p^p-1)) = 1.86196549645040699446... .

%t f[p_, e_] := p^(Ceiling[e/p]*p); 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])));}

%Y Cf. A072873, A365637.

%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

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Last modified September 11 23:47 EDT 2024. Contains 375842 sequences. (Running on oeis4.)