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

1,1

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

Links

Table of n, a(n) for n=1..60.

Formula

a(n) ~ n.

Example

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

Mathematica

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

Prog

(Magma) [n: n in [1..1000] | [7] subset Setseq(Set(Sort(&cat[Intseq(d): d in Divisors(n)])))]
(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(), 20)) # Chai Wah Wu, Dec 27 2021

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).

Sequence in context: A198390 A118905 A254064 * A376046 A092433 A056203

Adjacent sequences: A257221 A257222 A257223 * A257225 A257226 A257227

Keyword

nonn,base

Author

Jaroslav Krizek, May 05 2015

Extensions

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

Status

approved