A092122 Let R_{k}(m) = the digit reversal of m in base k (R_{k}(m) is written in base 10). Sequence gives numbers m such that m = Sum_{d|m, d>1} R_{d}(m).

6, 154, 310, 370, 2829, 3526, 15320, 20462, 1164789, 4336106, 5782196, 145582972

Offset: 1

Author

Naohiro Nomoto, Mar 30 2004

Keywords

• nonn
• base
• more

Examples

			m = 154 is a term: Sum_{d|154, d>1} R_{d}(154) = 89 + 10 + 34 + 11 + 7 + 2 + 1 = 154.
		

Crossrefs

Cf. A004086, A030101-A030108, A056960-A056963.

Programs

Python

from sympy import divisors
from sympy.ntheory import digits
def fd(d, b): return sum(di*b**i for i, di in enumerate(d[::-1]))
def R(k, n): return fd(digits(n, k)[1:][::-1], k)
def ok(n):
    s = 0
    for d in divisors(n, generator=True):
        if d == 1: continue
        s += R(d, n)
        if s > n: return False
    return n == s
print([k for k in range(1, 21000) if ok(k)]) # Michael S. Branicky, Nov 14 2022

Extensions

a(9)-a(12) from Michael S. Branicky, Nov 14 2022