A355790 Numbers that can be written as the product of two divisors greater than 1 such that the number is contained in the string concatenation of the divisors.

64, 95, 110, 210, 325, 510, 624, 640, 664, 950, 995, 1010, 1100, 1110, 3250, 3325, 5134, 6240, 6400, 6640, 6664, 7125, 7616, 8145, 9500, 9950, 9995, 11000, 11100, 11110, 20100, 21052, 21175, 25100, 26208, 32500, 33250, 33325, 35126, 50100, 51020, 51204, 51340, 57125, 62400, 64000, 65114

Offset: 1

Author

Scott R. Shannon, Jul 17 2022

Keywords

• nonn
• base

Examples

			64 is a term as 64 = 16 * 4 and "16" + "4" = "164" contains "64".
65114 is a term as 65114 = 4651 * 14 and "4651" + "14" = "465114" contains "65114".
See the attached text file for other examples.
		

Links

• Scott R. Shannon, Divisor product of the first 232 terms. These are all the numbers up to 50000000.

Crossrefs

Cf. A355791 (base-2), A030190, A210959, A027750, A355852, A339144, A341035, A342127, A027748, A048991, A330027, A077293.

Programs

Python

from sympy import divisors
def ok(n):
    s, divs = str(n), divisors(n)[1:-1]
    return any(s in str(d)+str(n//d) for d in divs)
print([k for k in range(1, 10**5) if ok(k)]) # Michael S. Branicky, Jul 27 2022