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A351475
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Multiplicative with a(prime(k)^e) = k^2 + e^2 for any k, e > 0.
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2
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1, 2, 5, 5, 10, 10, 17, 10, 8, 20, 26, 25, 37, 34, 50, 17, 50, 16, 65, 50, 85, 52, 82, 50, 13, 74, 13, 85, 101, 100, 122, 26, 130, 100, 170, 40, 145, 130, 185, 100, 170, 170, 197, 130, 80, 164, 226, 85, 20, 26, 250, 185, 257, 26, 260, 170, 325, 202, 290, 250
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OFFSET
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1,2
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COMMENTS
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This sequence gives the norm of the function f defined in A351464-A351465.
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LINKS
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FORMULA
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EXAMPLE
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For n = 42:
- 42 = 2 * 3 * 7 = prime(1)^1 * prime(2)^1 * prime(4)^1,
- a(42) = (1^2 + 1^2) * (2^2 + 1^2) * (4^2 + 1^2) = 170.
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MAPLE
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a:= proc(n) option remember; uses numtheory;
mul(pi(i[1])^2+i[2]^2, i=ifactors(n)[2])
end:
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MATHEMATICA
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f[p_, e_] := PrimePi[p]^2 + e^2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 15 2022 *)
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PROG
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(PARI) a(n) = { my (f=factor(n), p=f[, 1]~, e=f[, 2]~); prod (k=1, #p, primepi(p[k])^2 + e[k]^2) }
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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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