A062671 Every divisor (except 1) contains the digit 5.

5, 25, 53, 59, 125, 151, 157, 251, 257, 265, 295, 353, 359, 457, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 625, 653, 659, 751, 755, 757, 785, 853, 857, 859, 953, 1051, 1151, 1153, 1255, 1259, 1285, 1325, 1451, 1453, 1459, 1475, 1511

Offset: 1

Author

Erich Friedman, Jul 04 2001

Keywords

• base
• easy
• nonn

Examples

			25 has divisors 1, 5 and 25, all of which (except 1) contain the digit 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A062653, A062664, A062667, A062668, A062669, A062670, A062672, A062673, A062674, A062675, A062676, A062677, A062678, A062679, A062680.

Programs

Magma

[k:k in [2..1500]| forall{d:d in Set(Divisors(k)) diff {1}| 5 in Intseq(d)}]; // Marius A. Burtea, Nov 07 2019

Mathematica

fQ[n_, dgt_] := Union[ MemberQ[#, dgt] & /@ IntegerDigits@ Rest@ Divisors@ n][[1]]; Select[ Range[2, 1500], fQ[#, 5] &] (* Robert G. Wilson v, Jun 11 2014 *)

Python

from sympy import divisors
def ok(n): return all('5' in str(d) for d in divisors(n)[1:])
print(list(filter(ok, range(2, 1512)))) # Michael S. Branicky, May 25 2021

Extensions

Offset corrected by Amiram Eldar, Nov 07 2019