A340297 a(n) = (Sum of totatives of n) mod (Sum of primes dividing n with multiplicity).

1, 0, 0, 0, 1, 0, 4, 3, 6, 0, 3, 0, 6, 4, 0, 0, 6, 0, 8, 6, 6, 0, 6, 0, 6, 0, 3, 0, 0, 0, 6, 8, 6, 0, 6, 0, 6, 4, 1, 0, 0, 0, 5, 1, 6, 0, 10, 7, 8, 16, 12, 0, 2, 12, 9, 14, 6, 0, 0, 0, 6, 3, 4, 12, 4, 0, 17, 10, 0, 0, 0, 0, 6, 5, 11, 6, 0, 0, 6, 3, 6, 0, 0, 14, 6, 4, 9, 0, 1, 16, 26, 2, 6, 12, 2

Offset

2,7

Comments

a(n) = 0 if n is an odd prime.

If p is prime with p + A001414(x) > A000217(A001414(x))*x*A000010(x), then a(x*p) = A000217(A001414(x))*x*A000010(x) For example, a(2*p) = 6 if p is a prime >= 5, a(3*p) = 36 if p is a prime >= 37, and a(4*p) = 80 if p is a prime >= 79.

Links

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

Formula

a(n) = A023896(n) mod A001414(n).

Example

For n = 8, A023896(8) = 1+3+5+7 = 16 and A001414(n) = 2+2+2 = 6, so a(8) = 16 mod 6 = 4.

Maple

f:= proc(n) local F, t;
  F:= ifactors(n)[2];
  n*mul((t[1]-1)*t[1]^(t[2]-1), t=F)/2 mod add(t[1]*t[2], t=F);
end proc:
map(f, [$2..100]);

Crossrefs

Cf. A000217, A001414, A023896, A340299.

Sequence in context: A019322 A257301 A298801 * A369928 A016503 A319614

Adjacent sequences: A340294 A340295 A340296 * A340298 A340299 A340300

Keyword

nonn,look

Author

J. M. Bergot and Robert Israel, Jan 03 2021

Status

approved