OFFSET
1,1
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.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Marc Groz, Oct 02 2024
STATUS
approved