A342127 -id:A342127 - cp's OEIS frontend

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

Scott R. Shannon, Jul 17 2022

			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.

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

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

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

A342130 Decimal numbers m such that the product of the binary string of m and the binary string of m in reverse contains the binary string of m as a substring.

Original entry on oeis.org

0, 1, 2, 4, 8, 16, 27, 32, 54, 64, 108, 128, 139, 165, 256, 512, 815, 1024, 1630, 2048, 2821, 3167, 3693, 3941, 4096, 4747, 5642, 6334, 7737, 7881, 8192, 9494, 10837, 11284, 12479, 13363, 16384, 18988, 22568, 24669, 24958, 27945, 31205, 32768, 38869, 40861, 45136, 48367, 49338, 49535, 55121

Offset: 1

Scott R. Shannon, Mar 01 2021

All numbers of the form 2^k, k>=0, are in the sequence.

			8 is a term as bin(8)*reverse(bin(8)) = 100_2*1_2 = 100_2 contains '100' as a substring.
27 is a term as bin(27)*reverse(bin(27)) = 11011_2*11011_2 = 1011011001_2 contains '11011' as a substring.
108 is a term as bin(108)*reverse(bin(108)) = 1101100_2*11011_2 = 101101100100_2 contains '1101100' as a substring.
139 is a term as bin(139)*reverse(bin(139)) = 10001011_2*11010001_2 = 111000101111011_2 contains '10001011' as a substring.

Cf. A342127 (base 10), A305989, A007088, A000079, A203565, A332795.

strbin(x) = Str(fromdigits(binary(x), 10));
isok(m) = {my(p = m*fromdigits(Vecrev(binary(m)), 2)); #strsplit(strbin(p), strbin(m)) > 1;} \\ Michel Marcus, Mar 01 2021

cp's OEIS Frontend

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.

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