A232538 Numbers n such that (n(n+1)/2) modulo sigma(n) = n.

33, 136, 145, 261, 897, 1441, 2016, 2241, 2353, 3808, 4320, 7201, 17101, 26937, 30721, 32896, 46593, 70561, 148960, 151633, 169345, 174592, 208801, 400401, 578593, 712801, 803800, 1040401, 1103233, 1596673, 2265121, 2377089, 3330001, 4357153, 5953024, 5962321

Offset: 1

Author

Jaroslav Krizek, Nov 25 2013

Keywords

• nonn

Comments

Also numbers n such that antisigma(n) modulo sigma(n) = n. Antisigma(n) = A024816(n) = the sum of the nondivisors of n that are between 1 and n, sigma(n) = A000203(n) = the sum of the divisors of n.

Numbers n such that A232324(n) = n.

a(19) > 10^5.

Examples

			136 is in sequence because antisigma(136) mod sigma(136) = 9046 mod 270 = 136.
		

Crossrefs

Cf. A000203, A076617, A024816, A232324, A232540.

Programs

Mathematica

Select[Range[6*10^6],Mod[(#(#+1))/2,DivisorSigma[1,#]]==#&] (* Harvey P. Dale, Sep 12 2019 *)

PARI

isok(n) = (n*(n+1)/2 - sigma(n)) % sigma(n) == n; \\ Michel Marcus, Nov 25 2013

Formula

A232324(a(n)) = n.

Extensions

More terms from Michel Marcus, Nov 25 2013