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

1,1

Comments

A002385 (Palindromic primes) is a subsequence of this sequence.

Links

Table of n, a(n) for n=1..65.

Example

2151 is a term because 2151=3^2*239; 3+239=242; 3*239=717.

Mathematica

Select[Range[2, 1000], And @@ PalindromeQ /@ {Plus @@ (p = FactorInteger[#][[;; , 1]]), Times @@ p} &] (* Amiram Eldar, Mar 06 2023 *)

Prog

(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, ", ")))
(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

Crossrefs

Cf. A002113 (palindromes), A008472, A007947.

Sequence in context: A167620 A169935 A193498 * A239087 A378949 A095227

Adjacent sequences: A361178 A361179 A361180 * A361182 A361183 A361184

Keyword

nonn,base

Author

Alexandru Petrescu, Mar 06 2023

Status

approved