A260097 Numbers n = concat(s,t) such that n = sigma(s*t), where sigma(x) is the sum of the divisors of x.

124, 2352, 2604, 6804, 15240, 63180, 225302, 632400, 1531152, 2537040, 4592588, 7160400, 7603680, 26100144, 26378352, 31492032, 33747840, 49447728, 88385040, 104941200, 162496048, 175600040, 197499456, 403242624, 483741216, 797091840, 2077442640, 2942021520, 4045874976, 4828299840

Offset: 1

Author

Paolo P. Lava, Jul 16 2015

Keywords

• nonn
• base

Examples

			124 = concat(12,4) and sigma(12*4) = sigma(48) = 124.
2352 = concat(23,52) and sigma(23*52) = sigma(1196) = 2352.
		

Crossrefs

Cf. A000203, A253824, A253825.

Programs

Maple

with(numtheory); P:=proc(q) local a,b,i,n,p; for n from 1 to q do
for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i;
if sigma(a*b)=n then print(n); break; fi; od; od; end: P(10^9);

PARI

isok(n) = {len = #Str(n); for (k=1, len-1, na = n\10^k; nb = n % 10^k; if (nb && (n == sigma(na*nb)), return (1)); ); } \\ Michel Marcus, Jul 17 2015

Python

from sympy import divisor_sigma
A260097_list= []
for n in range(11,10**6):
    s = str(n)
    for l in range(1, len(s)):
        m = int(s[:l])*int(s[l:])
        if m > 0 and n == divisor_sigma(m):
            A260097_list.append(n)
            break # Chai Wah Wu, Jul 18 2015

Extensions

a(14)-a(15) from Chai Wah Wu, Jul 18 2015

a(16)-a(28) from Lars Blomberg, Jul 21 2015

a(29)-a(30) from Giovanni Resta, Jul 24 2015