A237719 Numbers n such that k(n) = (n(n+1)/2 mod n) = (antisigma(n) mod n) + (sigma(n) mod n).

1, 2, 6, 12, 18, 20, 24, 28, 30, 40, 42, 54, 56, 66, 70, 78, 80, 88, 100, 102, 104, 112, 114, 120, 126, 138, 140, 150, 160, 162, 174, 176, 180, 186, 196, 198, 200, 204, 208, 220, 222, 224, 228, 234, 240, 246, 258, 260, 272, 276, 282, 294, 304, 306, 308, 318, 320

Offset

1,2

Comments

Numbers n such that k(n) = A142150(n) = A229110(n) + A054024(n).

Numbers n such that k(n) = (A000217(n) mod n) = (A024816(n) mod n) + (A000203(n) mod n).

k(n) = 0 for odd n, k(n) = n/2 for even n.

If there are any odd multiply-perfect numbers, they are members of this sequence.

If there is no odd multiply-perfect number, then:

(1) the only odd number in this sequence is 1,

(2) corresponding sequence of numbers k(n): {0; a(n) / 2 for n > 1}.

Supersequence of A159907, A007691 and A000396.

Links

Table of n, a(n) for n=1..57.

Example

12 is in the sequence because k(12) = (12*(12+1)/2) mod 12 = antisigma(12) mod 12 + sigma(12) mod 12; k(12) = 6 = 4 + 2 = n/2.

Prog

(Magma) [n: n in [1..320] | IsZero(n*(n+1)div 2 mod n - SumOfDivisors(n) mod n - (n*(n+1)div 2-SumOfDivisors(n)) mod n)]

Crossrefs

Cf. A000203, A000217, A024816, A054024, A142150, A229110.

Sequence in context: A299112 A154030 A055560 * A369383 A108727 A138630

Adjacent sequences: A237716 A237717 A237718 * A237720 A237721 A237722

Keyword

nonn

Author

Jaroslav Krizek, Mar 16 2014

Status

approved