A257224 Numbers that have at least one divisor containing the digit 7 in base 10.

7, 14, 17, 21, 27, 28, 34, 35, 37, 42, 47, 49, 51, 54, 56, 57, 63, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 84, 85, 87, 91, 94, 97, 98, 102, 105, 107, 108, 111, 112, 114, 117, 119, 126, 127, 133, 134, 135, 136, 137, 140, 141, 142, 144, 146, 147, 148

Offset: 1

Author

Jaroslav Krizek, May 05 2015

Keywords

• nonn
• base
• changed

Comments

Numbers k whose concatenation of divisors A037278(k), A176558(k), A243360(k) or A256824(k) contains a digit 7.

A011537 (numbers that contain a 7) is a subsequence. - Michel Marcus, May 25 2015

Examples

			14 is in sequence because the list of divisors of 14: (1, 2, 7, 14) contains digit 7.
		

Crossrefs

Cf. A037278, A176558, A243360, A256824.

Cf. similar sequences with another digit: A209932 (0), A000027 (1), A257219 (2), A257220 (3), A257221 (4), A257222 (5), A257223 (6), A257225 (8), A257226 (9).

Programs

Magma

[n: n in [1..1000] | [7] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))];

Mathematica

Select[Range@108, Part[Plus @@ DigitCount@ Divisors@ #, 7] > 0 &]

PARI

is(n)=fordiv(n, d, if(setsearch(Set(digits(d)), 7), return(1))); 0

Python

from itertools import count, islice
from sympy import divisors
def A257224_gen(): return filter(lambda n:any('7' in str(d) for d in divisors(n, generator=True)), count(1))
A257224_list = list(islice(A257224_gen(), 60)) # Chai Wah Wu, Dec 27 2021

Formula

a(n) ~ n.

Extensions

Mathematica and PARI programs with assistance from Michael De Vlieger and Charles R Greathouse IV, respectively.