A352996 - OEIS

A352996

a(n) = n*(n+1)/2 mod (sum (with multiplicity) of prime factors of n).

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

2,3

COMMENTS

If n is an odd prime, a(n) = 0.

If n is prime, a(n^2) = n.

LINKS

Robert Israel, Table of n, a(n) for n = 2..10000

FORMULA

a(n) = A000217(n) mod A001414(n).

EXAMPLE

For n = 6, A000217(6) = 6*7/2 = 21 and A001414(6) = 2+3 = 5, so a(6) = 21 mod 5 = 1.