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Composite numbers in A265640.
1

%I #23 Oct 05 2024 00:39:50

%S 4,8,9,12,16,18,20,25,27,28,32,36,44,45,48,49,50,52,63,64,68,72,75,76,

%T 80,81,92,98,99,100,108,112,116,117,121,124,125,128,144,147,148,153,

%U 162,164,169,171,172,175,176,180,188,192,196,200,207,208,212,225,236,242,243,244,245

%N Composite numbers in A265640.

%C 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.

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

%H Michael S. Branicky, <a href="/A376715/b376715.txt">Table of n, a(n) for n = 1..10000</a>

%e 44 is a term, since 44 = 2*11*2.

%e 52 is a term, since 52 = 2*13*2.

%e 180 is a term, since 180 = 2*3*5*3*2.

%e 676 is a term, since 676 = 2*13*13*2.

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

%o (Python)

%o from math import isqrt

%o from sympy.ntheory.factor_ import core, isprime

%o def ok(n): return n > 3 and (isqrt(n)**2 == n or (not isprime(n) and isprime(core(n))))

%o print([k for k in range(1, 246) if ok(k)]) # _Michael S. Branicky_, Oct 03 2024

%Y Intersection of A002808 and A265640.

%Y Cf. A013929, A265640.

%K nonn,base

%O 1,1

%A _Marc Groz_, Oct 02 2024