A227231 Numbers k such that antisigma(k) mod k = k - 1.

1, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 36, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263

Offset: 1

Author

Jaroslav Krizek, Sep 26 2013

Keywords

• nonn

Comments

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

Union of A065091 (odd primes) and sequence nonprimes 1, 4, 36, ... (all terms < 10^5).

No more composite terms to 10^10. - Charles R Greathouse IV, Nov 02 2014

Examples

			antisigma(36) mod 36 => 575 mod 36 = 35.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A024816 (antisigma(n)), A065091, A229110 (antisigma(n) mod n).

Programs

Magma

[n: n in [1..1000] | n-1 eq ((n*(n+1) div 2-SumOfDivisors(n)) mod n)]; // Jaroslav Krizek, May 28 2014

PARI

is(n)=(n*(n+1)/2-sigma(n)+1)%n==0 \\ Charles R Greathouse IV, Nov 02 2014