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A237719 Numbers n such that k(n) = (n(n+1)/2 mod n) = (antisigma(n) mod n) + (sigma(n) mod n). 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A108727 A138630 A026229

Adjacent sequences:  A237716 A237717 A237718 * A237720 A237721 A237722

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Mar 16 2014

STATUS

approved

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Last modified September 24 18:55 EDT 2022. Contains 356949 sequences. (Running on oeis4.)