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

Author

Zdenek Cervenka, Feb 21 2022

Keywords

• nonn
• base

Examples

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

Crossrefs

Cf. A007953, A032741, A057531.

Programs

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 &]

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);

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