OFFSET
1,1
COMMENTS
a(28) > 10^11. - Hiroaki Yamanouchi, Sep 26 2015
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 1..27
EXAMPLE
6396 = concat(63,96) -> sigma(63)-63 = 41, sigma(96)-96 = 156 and 41*156 = 6396.
20680 = concat(20,680) -> sigma(20)-20 = 22, sigma(680)-680 = 940 and 22*940 = 20680.
124416 = concat(12,4416) -> sigma(12)-12 = 16, sigma(4416)-4416 = 7776 and 16*7776 = 124416.
567816 = concat(567,816) -> sigma(567)-567 = 410, sigma(816)-816 = 1416 and 401*1416 = 567816.
MAPLE
with(numtheory): P:=proc(q) local s, t, k, n;
for n from 1 to q do for k from 1 to ilog10(n) do s:=n mod 10^k; t:=trunc(n/10^k); if s*t>0 then if (sigma(s)-s)*(sigma(t)-t)=n
then print(n); break; fi; fi; od; od; end: P(10^6);
MATHEMATICA
fQ[n_] := Block[{idn = IntegerDigits@ n, lng = Floor@ Log10@ n}, MemberQ[ Table[s = FromDigits@ Take[idn, {1, i}]; t = FromDigits@ Take[idn, {i + 1, lng + 1}]; (DivisorSigma[1, s] - s) (DivisorSigma[1, t] - t), {i, lng}], n]]; k = 1; lst = {}; While[k < 100000001, If[fQ@ k, AppendTo[lst, k]; Print@ k]; k++] (* Robert G. Wilson v, Jan 26 2015 *)
PROG
(PARI) isok(n) = {len = #Str(n); for (k=1, len-1, na = n\10^k; nb = n % 10^k; if (nb && (n == (sigma(na)-na)*(sigma(nb)-nb)), return (1)); ); } \\ Michel Marcus, Jan 15 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jan 15 2015
EXTENSIONS
a(8) & a(9) from Robert G. Wilson v, Jan 26 2015
a(10)-a(24) from Hiroaki Yamanouchi, Sep 26 2015
STATUS
approved