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 A253824 Numbers n = concat(s,t) such that n = sigma(s) * sigma(t), where sigma(x) is the sum of the divisors of x. 9
 540, 2352, 28224, 82890, 737856, 1524096, 1531152, 3429216, 17062920, 22264200, 23268600, 49447728, 104941200, 162496048, 197499456, 267450144, 502334784, 619672032, 2347826040, 2942021520, 4045874976, 4302305280, 9876226752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..23. EXAMPLE 540 = concat(5,40) -> sigma(5) = 6, sigma(40) = 90 and 6*90 = 540. 2352 = concat(23,52) -> sigma(23) = 24, sigma(52) = 98 and 24*98 = 2352. 28224 = concat(28,224) -> sigma(28) = 56, sigma(224) = 504 and 56*504 = 28222. 82890 = concat(8,2890) -> sigma(8) = 15, sigma(2890) = 5526 and 15*5526 = 82890. 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)*sigma(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[ DivisorSigma[1, FromDigits@ Take[ idn, {1, i}]] DivisorSigma[1, FromDigits@ Take[ idn, {i + 1, lng + 1}]], {i, lng}], n]]; k = 1; lst = {}; While[k < 1310000001, If[fQ@ k, AppendTo[ lst, k]; Print@ k]; k++] (* Robert G. Wilson v, Jan 19 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)*sigma(nb)), return (1)); ); } \\ Michel Marcus, Jan 15 2015 CROSSREFS Cf. A000203, A159000, A253825, A260144. Sequence in context: A298685 A185463 A069474 * A218414 A328133 A146123 Adjacent sequences: A253821 A253822 A253823 * A253825 A253826 A253827 KEYWORD nonn,base,more AUTHOR Paolo P. Lava, Jan 15 2015 EXTENSIONS a(8) from Michel Marcus, Jan 15 2015 a(9)-a(17) from Robert G. Wilson v, Jan 18 2015 Missing a(14) and a(19)-a(23) from Giovanni Resta, Jul 17 2015 STATUS approved

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Last modified April 15 05:10 EDT 2024. Contains 371667 sequences. (Running on oeis4.)