A280987 {Concatenation n, n-1, n-2, ...3,2,1} mod sigma(n).

0, 0, 1, 2, 3, 9, 1, 6, 4, 1, 9, 21, 1, 9, 9, 16, 9, 24, 1, 33, 17, 1, 9, 21, 0, 9, 1, 41, 21, 33, 17, 6, 33, 19, 33, 25, 25, 21, 1, 1, 33, 81, 17, 21, 45, 1, 33, 85, 49, 69, 57, 77, 27, 81, 1, 81, 1, 1, 21, 57, 59, 81, 33, 60, 21, 33, 45, 51, 81, 1, 9, 66, 41, 9, 97, 1, 81, 81, 1, 57, 117, 73, 33, 145

Offset: 1

Author

Indranil Ghosh, Jan 12 2017

Keywords

• nonn
• base

Examples

			For n = 11, A000422(n) mod sigma(n) = 1110987654321 mod 12 = 9. S0 a(11) = 9.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000422, A114795.

Programs

Mathematica

Table[Mod[FromDigits[Flatten[IntegerDigits/@Range[n,1,-1]]],DivisorSigma[ 1,n]],{n,90}] (* Harvey P. Dale, Jul 01 2020 *)

Python

def sigma(n):
    s=0
    for i in range(1,n+1):
        if n%i==0:
            s+=i
    return s
def C(n):
    s=""
    for i in range(n,0,-1):
        s+=str(i)
    return int(s)
for i in range(1,101):
    print(i, C(i)%sigma(i))

Python

from sympy import divisor_sigma
def A280987(n): return int(''.join(map(str, range(n, 0, -1)))) % divisor_sigma(n) # David Radcliffe, Aug 08 2025

Formula

a(n) = A000422(n) mod A000203(n).