A229114 Numbers k such that antisigma(k) mod k = antisigma(k+1) mod (k+1).

1, 8, 27, 3115, 3451, 4725, 10611, 15951, 20155, 27643, 74875, 2767675, 18390564, 27923284, 50293331, 425018875, 897002491, 10561657872, 15193530235, 20939306635, 40882585915, 80585844499

Offset: 1

Author

Jaroslav Krizek, Sep 26 2013

Keywords

• nonn
• more

Comments

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

Numbers k such that A229110(k) = A229110(k+1).

For k < 10^8, 2 is the only number such that sigma(k) mod k = sigma(k+1) mod (k+1).

a(23) > 10^11. - Donovan Johnson, Sep 27 2013

Examples

			a(3) = 27 because antisigma(27) mod 27 = 338 mod 27 = antisigma(28) mod 28 = 350 mod 28 = 14.
		

Crossrefs

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

Programs

PARI

s=1; r=0; for(n=1, 10^9, n1=n+1; s=s+n1; r1=(s-sigma(n1))%n1; if(r==r1, print(n)); r=r1) /* Donovan Johnson, Sep 27 2013 */

Extensions

a(12)-a(22) from Donovan Johnson, Sep 27 2013