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A308486 Numbers such that the sum of divisors divides the concatenation (in ascending order) of divisors. 2
1, 2, 6, 10, 40, 98, 112, 120, 1904, 2680, 4040, 4128, 5136, 9920, 12224, 17900, 20880, 27800, 44160, 55520, 57121, 62240, 86866, 158880, 178120, 1431808, 1773920, 1825280, 1918640, 3751328, 5452288, 6749600, 7262120, 7446720, 9916832, 17777440, 46168000, 101829808 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Numbers k such that A000203(k) divides A037278(k). - Michel Marcus, Jun 02 2019.
Similar to A308533 where anti-divisors are considered.
LINKS
EXAMPLE
Divisors of 98 are 1, 2, 7, 14, 49, 98 and their sum is sigma(98) = 171. Then, 127144998 / 171 = 743538.
MAPLE
with(numtheory): P:=proc(q) local n; for n from 1 to q do if frac(parse(cat(op(sort([op(divisors(n))]))))/sigma(n))=0 then
print(n); fi; od; end: P(10^6);
MATHEMATICA
Select[Range[10^6], Mod[FromDigits@ Flatten@ IntegerDigits[#], Total@ #] == 0 &@ Divisors@ # &] (* Michael De Vlieger, Jun 03 2019 *)
PROG
(Magma) k:=1; sol:=[];
for u in [1..10000000] do D:=Divisors(u); conc:=D[1];
for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]); conc:=10^a1*conc+D[u1];
end for;
if conc mod SumOfDivisors(u) eq 0 then sol[k]:=u; k:=k+1; end if;
end for;
sol; // Marius A. Burtea, Jun 01 2019
(PARI) concd(n) = my(d=divisors(n), s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ A037278
isok(n) = (concd(n) % sigma(n)) == 0; \\ Michel Marcus, Jun 05 2019
CROSSREFS
Sequence in context: A258079 A027165 A111414 * A202533 A275700 A258899
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, May 31 2019
EXTENSIONS
a(30)-a(38) from Giovanni Resta, May 31 2019
STATUS
approved

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Last modified July 22 16:15 EDT 2024. Contains 374540 sequences. (Running on oeis4.)