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

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.

Maple

seq((n*(n+1)/2) mod add(t[1]*t[2], t=ifactors(n)[2]), n=2..100);

Mathematica

a[n_] := Mod[n*(n + 1)/2, Plus @@ Times @@@ FactorInteger[n]]; Array[a, 100, 2] (* Amiram Eldar, Apr 15 2022 *)

Prog

(Python)
from sympy import factorint
def a(n): return (n*(n+1)//2)%sum(p*e for p, e in factorint(n).items())
print([a(n) for n in range(2, 98)]) # Michael S. Branicky, Apr 24 2022

Crossrefs

Cf. A352989, A352990, A352997.

Sequence in context: A036853 A036852 A260941 * A329918 A281442 A256038

Adjacent sequences: A352993 A352994 A352995 * A352997 A352998 A352999

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 14 2022

Status

approved