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A352996
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a(n) = n*(n+1)/2 mod (sum (with multiplicity) of prime factors of n).
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4
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1, 0, 2, 0, 1, 0, 0, 3, 6, 0, 1, 0, 6, 0, 0, 0, 3, 0, 3, 1, 6, 0, 3, 5, 6, 0, 10, 0, 5, 0, 8, 1, 6, 6, 6, 0, 6, 12, 6, 0, 3, 0, 0, 1, 6, 0, 10, 7, 3, 6, 1, 0, 0, 4, 10, 3, 6, 0, 6, 0, 6, 1, 4, 3, 3, 0, 15, 23, 7, 0, 0, 0, 6, 3, 5, 15, 3, 0, 3, 9, 6, 0, 0, 3, 6, 20, 6, 0, 0, 6, 12, 19, 6, 0, 2, 0
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OFFSET
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2,3
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COMMENTS
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If n is an odd prime, a(n) = 0.
If n is prime, a(n^2) = n.
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LINKS
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FORMULA
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EXAMPLE
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For n = 6, A000217(6) = 6*7/2 = 21 and A001414(6) = 2+3 = 5, so a(6) = 21 mod 5 = 1.
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MAPLE
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seq((n*(n+1)/2) mod add(t[1]*t[2], t=ifactors(n)[2]), n=2..100);
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MATHEMATICA
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a[n_] := Mod[n*(n + 1)/2, Plus @@ Times @@@ FactorInteger[n]]; Array[a, 100, 2] (* Amiram Eldar, Apr 15 2022 *)
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PROG
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(Python)
from sympy import factorint
def a(n): return (n*(n+1)//2)%sum(p*e for p, e in factorint(n).items())
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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