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A166648
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Totally multiplicative sequence with a(p) = 8*(p+1) for prime p.
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1
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1, 24, 32, 576, 48, 768, 64, 13824, 1024, 1152, 96, 18432, 112, 1536, 1536, 331776, 144, 24576, 160, 27648, 2048, 2304, 192, 442368, 2304, 2688, 32768, 36864, 240, 36864, 256, 7962624, 3072, 3456, 3072, 589824, 304, 3840, 3584, 663552, 336, 49152
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (8*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)+1)^e(k).
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MATHEMATICA
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a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*8^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 21 2016 *)
f[p_, e_] := (8*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 8*(f[k, 1]+1)); factorback(f); } \\ Michel Marcus, May 21 2016
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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