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

Author

Jaroslav Krizek, Mar 16 2014

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

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

Programs

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)]