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 A356192 a(n) is the smallest cubefull exponentially odd number (A335988) that is divisible by n. 12
 1, 8, 27, 8, 125, 216, 343, 8, 27, 1000, 1331, 216, 2197, 2744, 3375, 32, 4913, 216, 6859, 1000, 9261, 10648, 12167, 216, 125, 17576, 27, 2744, 24389, 27000, 29791, 32, 35937, 39304, 42875, 216, 50653, 54872, 59319, 1000, 68921, 74088, 79507, 10648, 3375, 97336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differs from A053149 and A356193 at n=16. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(p^e) = p^max(e,3) if e is odd and p^(e+1) otherwise. a(n) = n iff n is in A335988. a(n) = A356191(n) iff n is a powerful number (A001694). Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + (3*p^2-1)/(p^3*(p^2-1))) = 1.69824776889117043774... . Sum_{k=1..n} a(k) ~ c * n^4, where c = (zeta(6)/4) * Product_{p prime} (1 - 1/p^2 + 1/p^5 - 2/p^6 + 1/p^8 + 1/p^9 - 1/p^10) = 0.1559368144... . - Amiram Eldar, Nov 13 2022 MATHEMATICA f[p_, e_] := If[OddQ[e], p^Max[e, 3], p^(e + 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] PROG (PARI) a(n) = {my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]%2, f[i, 1]^max(f[i, 2], 3), f[i, 1]^(f[i, 2]+1)))}; CROSSREFS Cf. A001694, A013664, A268335, A335988. Similar sequences: A053149, A053143, A053167, A066638, A087320, A087321, A197863, A356191, A356193, A356194. Sequence in context: A005064 A056551 A356193 * A367934 A053149 A102637 Adjacent sequences: A356189 A356190 A356191 * A356193 A356194 A356195 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Jul 29 2022 STATUS approved

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Last modified May 30 15:53 EDT 2024. Contains 372968 sequences. (Running on oeis4.)