A257221 Numbers that have at least one divisor containing the digit 4 in base 10.

4, 8, 12, 14, 16, 20, 24, 28, 32, 34, 36, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 54, 56, 60, 64, 68, 70, 72, 74, 76, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 108, 112, 114, 116, 120, 123, 124, 126, 128, 129, 132, 134, 135, 136, 138, 140, 141

Offset: 1

Author

Jaroslav Krizek, Apr 20 2015

Keywords

• nonn
• base

Comments

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 4.

Sequences of numbers k whose concatenation of divisors contains a digit j in base 10 for 0 <= j <= 9: A209932 for j = 0, A000027 for j = 1, A257219 for j = 2, A257220 for j = 3, A257221 for j = 4, A257222 for j = 5, A257223 for j = 6, A257224 for j = 7, A257225 for j = 8, A257226 for j = 9.

Examples

			16 is in sequence because the list of divisors of 16: (1, 2, 4, 8, 16) contains digit 4.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037278, A176558, A243360, A256824.

Programs

Magma

[n: n in [1..1000] | [4] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]

Mathematica

Select[Range@ 141, Part[Plus @@ DigitCount@ Divisors@ #, 4] > 0 &] (* Michael De Vlieger, Apr 20 2015 *)
Select[Range[200],Count[Flatten[IntegerDigits/@Divisors[#]],4]>0&] (* Harvey P. Dale, May 05 2022 *)

PARI

is(n)=fordiv(n,d, if(setsearch(Set(digits(d)),4), return(1))); 0 \\ Charles R Greathouse IV, Apr 30 2015

Formula

a(n) ~ n. - Charles R Greathouse IV, Apr 30 2015