A351842 Numbers whose sum of digits and number of proper divisors are equal.

21, 32, 50, 70, 111, 162, 168, 201, 212, 232, 250, 308, 322, 380, 384, 405, 416, 430, 456, 546, 610, 650, 690, 740, 744, 812, 832, 870, 980, 1004, 1011, 1015, 1053, 1101, 1105, 1222, 1316, 1352, 1365, 1460, 1464, 1482, 1510, 1518, 1550, 1554, 1590, 1608, 1752

Offset

1,1

Links

Table of n, a(n) for n=1..49.

Example

21 is a term since its digits sum to 2 + 1 = 3 and it has three proper divisors (1, 3, and 7).

Maple

S := n -> add(convert(n, base, 10)):
PD := n -> nops(NumberTheory[Divisors](n)) - 1:
a := n -> select(x -> S(x) = PD(x), [seq(1..n)])

Mathematica

Select[Range[1, 1700], Total[IntegerDigits[#]] == Length[Divisors[#]] - 1 &]

Prog

(Python)
from sympy import divisor_count
def ok(n): return sum(map(int, str(n))) == divisor_count(n) - 1
print([k for k in range(1753) if ok(k)]) # Michael S. Branicky, Feb 21 2022
(PARI) isok(m) = sumdigits(m) == numdiv(m) - 1; \\ Michel Marcus, Feb 21 2022
(PARI) list(nn) = forcomposite(n=1, nn, if (sumdigits(n) == (numdiv(n) - 1), print1(n, ", ")));
list(1700);

Crossrefs

Cf. A007953, A032741, A057531.

Sequence in context: A319477 A035137 A261910 * A075110 A219684 A219881

Adjacent sequences: A351839 A351840 A351841 * A351843 A351844 A351845

Keyword

nonn,base

Author

Zdenek Cervenka, Feb 21 2022

Status

approved