A359444 a(n) is the least number that has exactly n divisors with sum of digits n.

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

Links

Table of n, a(n) for n=1..32.

Rémy Sigrist, C program

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

Cf. A007953, A359959.

Sequence in context: A362268 A116530 A219830 * A041780 A041782 A041784

Adjacent sequences: A359441 A359442 A359443 * A359445 A359446 A359447

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