A376715 Composite numbers in A265640.

4, 8, 9, 12, 16, 18, 20, 25, 27, 28, 32, 36, 44, 45, 48, 49, 50, 52, 63, 64, 68, 72, 75, 76, 80, 81, 92, 98, 99, 100, 108, 112, 116, 117, 121, 124, 125, 128, 144, 147, 148, 153, 162, 164, 169, 171, 172, 175, 176, 180, 188, 192, 196, 200, 207, 208, 212, 225, 236, 242, 243, 244, 245

Offset: 1

Author

Marc Groz, Oct 02 2024

Keywords

• nonn
• base

Comments

The first dozen terms match those of A013929; 40 is the smallest number that is not squarefree and therefore in A013929 but whose prime factors cannot be artranged to form a palindrome. Other examples are 54, 56, and 60. On the other hand, the current sequence is a proper subset of both A013929 and A265640.

Note that, like A265640, this is not a base-dependent sequence.

Examples

			44 is a term, since 44 = 2*11*2.
52 is a term, since 52 = 2*13*2.
180 is a term, since 180 = 2*3*5*3*2.
676 is a term, since 676 = 2*13*13*2.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A002808 and A265640.

Cf. A013929, A265640.

Programs

PARI

isok(n)=my(f=factor(n)[,2]); vecsum(f)>=2 && #select(e->e%2, f)<=1 \\ Andrew Howroyd, Oct 02 2024

Python

from math import isqrt
from sympy.ntheory.factor_ import core, isprime
def ok(n): return n > 3 and (isqrt(n)**2 == n or (not isprime(n) and isprime(core(n))))
print([k for k in range(1, 246) if ok(k)]) # Michael S. Branicky, Oct 03 2024