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A359444
a(n) is the least number that has exactly n divisors with sum of digits n.
2
1, 20, 60, 440, 1400, 420, 11200, 11440, 324, 58520, 180880, 18480, 585200, 523600, 114240, 1133440, 2420600, 17820, 9634240, 9529520, 1659840, 33353320, 71380400, 4748100, 178890320, 228388160, 671328, 413736400, 1081662400, 73670520, 3301916800, 2325202880
OFFSET
1,2
COMMENTS
a(30) = 73670520, a(36) = 12598740. - Daniel Suteu, Jan 22 2023
a(28) <= 8704721480, a(29) <= 24870632800. # Robert Israel, Jan 23 2023
EXAMPLE
a(1) = 1 because 1 has 1 divisor, 1, with digit sum 1.
a(2) = 20 because 20 has 2 divisors, 2 and 20, with digit sum 2.
a(3) = 60 because 60 has 3 divisors, 3, 12 and 30, with digit sum 3.
a(4) = 440 because 440 has 4 divisors, 4, 22, 40 and 220, with digit sum 4.
MAPLE
f:= proc(n) local D;
D:= map(t -> convert(convert(t, base, 10), `+`), convert(numtheory:-divisors(n), list));
select(t -> numboccur(t, D) = t, convert(D, set))
end proc:
N:= 20: # for a(1)..a(N)
V:= Vector(N): count:= 0:
for n from 1 while count < N do
for w in f(n) do
if w <= N and V[w] = 0 then
V[w]:= n; count:= count+1
fi
od od:
convert(V, list);
PROG
(PARI) is(n, m)=vecsum(apply(x->x==m, apply(vecsum, apply(digits, divisors(n)))))==m;
a(m)=for(x=1, +oo, is(x, m)&&return(x)); \\ R. J. Cano, Jan 22 2023
(C) See Links section.
CROSSREFS
Sequence in context: A362268 A116530 A219830 * A041780 A041782 A041784
KEYWORD
nonn,base
AUTHOR
Robert Israel, Jan 21 2023
EXTENSIONS
a(19)-a(27) from Daniel Suteu, Jan 22 2023
More terms from Rémy Sigrist, Jan 27 2023
STATUS
approved