A337733 Numbers that can be written as (k + sum of digits of k) for some k, also as (m + product of digits of m) for some m, and finally as (q * product of digits of q) for some q.

4, 16, 24, 56, 81, 88, 138, 144, 192, 242, 250, 297, 366, 408, 456, 516, 520, 522, 564, 575, 704, 744, 777, 795, 819, 884, 900, 912, 966, 1008, 1053, 1071, 1080, 1104, 1134, 1250, 1312, 1316, 1375, 1512, 1520, 1608, 1644, 1680, 1712, 1778, 1928, 1950, 2025, 2048, 2072

Offset: 1

Author

Bernard Schott, Sep 18 2020

Keywords

• nonn
• base

Comments

Equivalently, Bogotá numbers that are not Colombian and that can be written as (m + product of digits of m) for some m.

The only primes that can belong to this sequence are repunits > 11 whose indices are in A004023. It is known that these primes belong to A336983, but do they belong also to A337718?

Examples

			4 = 2 + 2 = 2 + 2 = 2 * 2;
16 = 8 + 8 = 8 + 8 = 4 * 4;
24 = 21 + (2+1) = 17 + (1*7) = 12 * (1*2);
56 = 46 + (4+6) = 51 + (5*1) = 14 * (1*4);
81 = 72 + (7+2) = 63 + (6*3) = 9 * 9.
		

Links

• Index to sequences related to Colombian numbers.

Crossrefs

Intersection of A176995, A336826 and A337718.

Intersection of A336983 and A337718.

Cf. A004023, A337139.

Programs

Mathematica

m = 2100; Select[Intersection @@ Union /@ Transpose[Table[{n + Plus @@ (d = IntegerDigits[n]), n + (p = Times @@ d), n*p}, {n, 1, m}]], # <= m &] (* Amiram Eldar, Sep 18 2020 *)

PARI

isok(m) = {if (m==0, return (1)); for (k=1, m,  if (k+vecprod(digits(k)) == m, return (1)); ); } \\ A337718
listb(nn) = Vec(setintersect(Set(vector(nn, k, k+sumdigits(k))), Set(vector(nn, k, k*vecprod(digits(k)))))); \\ A336983
lista(nn) = select(x->isok(x), listb(nn)); \\ Michel Marcus, Sep 18 2020

Extensions

More terms from Michel Marcus, Sep 18 2020