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 A253825 Numbers n = concat(s,t) such that n = (sigma(s)-s) * (sigma(t)-t), where sigma(x)-x is the sum of the aliquot parts of x. 9
 6396, 20680, 124416, 567816, 1719480, 7593432, 10538040, 36382320, 107277800, 123251968, 166601760, 327844840, 933363000, 1286859804, 2524125184, 3398418000, 4561432920, 4566915540, 4911440776, 7097433536, 16913792670, 20565608940, 21099997800, 27639552000 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A001065, A000203, A253824. Sequence in context: A278187 A206125 A322935 * A186068 A186064 A251454 Adjacent sequences: A253822 A253823 A253824 * A253826 A253827 A253828 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

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Last modified September 12 11:34 EDT 2024. Contains 375851 sequences. (Running on oeis4.)