A361181 Numbers such that both sum and product of the prime factors (without multiplicity) are palindromic.
2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 16, 18, 24, 25, 27, 32, 36, 48, 49, 54, 64, 72, 81, 96, 101, 108, 121, 125, 128, 131, 144, 151, 162, 181, 191, 192, 216, 243, 256, 288, 313, 324, 343, 353, 373, 383, 384, 432, 486, 512, 576, 625, 648, 717, 727, 729, 757, 768, 787, 797, 864, 919, 929, 972, 989
Offset: 1
Examples
2151 is a term because 2151=3^2*239; 3+239=242; 3*239=717.
Programs
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Mathematica
Select[Range[2, 1000], And @@ PalindromeQ /@ {Plus @@ (p = FactorInteger[#][[;; , 1]]), Times @@ p} &] (* Amiram Eldar, Mar 06 2023 *) -
PARI
ispal(n) = my(d=digits(n)); d == Vecrev(d) \\ A002113 for(n=2,1e5; f=factor(n); sf=0; mf=1;for(j=1,#f~, sf+=f[j,1]; mf*=f[j,1]); if(ispal(sf) && ispal(mf),print1(n,", ")))
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Python
from math import prod from sympy import factorint def ispal(n): return (s:=str(n)) == s[::-1] def ok(n): return ispal(sum(f:=factorint(n))) and ispal(prod(f)) print([k for k in range(2, 999) if ok(k)]) # Michael S. Branicky, Mar 06 2023
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