A244324 Numbers n such that floor(antisigma(n) / n) = antisigma(n) mod n.

1, 2, 15, 20, 104, 207, 464, 650, 1023, 1952, 2975, 19359, 130304, 147455, 522752, 1207359, 5017599, 8382464

Offset: 1

Author

Jaroslav Krizek, Jun 25 2014

Keywords

• nonn

Comments

Antisigma(n) = A024816(n) = sum of numbers less than n which do not divide n.

Also numbers n such that there is some number k > 0 with property: antisigma(n) = k*(n+1). Corresponding values of numbers k: 0, 0, 6, 8, 50, 102, 230, 323, 510, 974, 1486, 9678, …

Numbers n such that A244325(n) = A229110(n).

Examples

			Antisigma(19359) = 187366080 = 9678*19359 + 9678.
		

Crossrefs

Cf. A024816, A244325, A229110.

Programs

Magma

[n: n in [1..1000000] | u eq 0 where u is (Floor((((n*(n+1)) div 2  - SumOfDivisors(n)) div n))) - (((((n*(n+1)) div 2)-SumOfDivisors(n)) mod (n)))]

PARI

isok(n) = my(as = n*(n+1)/2 - sigma(n)); (as\n == as % n); \\ Michel Marcus, Jun 26 2014

Extensions

a(16)-a(18) from Michel Marcus, Jun 26 2014