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A327749 Natural numbers whose sum of prime factors (with repetition) is palindromic in base 10.

%I A327749 #31 Sep 08 2022 08:46:24
%S A327749 1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,18,20,24,27,28,40,45,48,54,57,62,
%T A327749 85,101,102,106,116,121,123,131,151,181,182,191,194,218,259,260,278,
%U A327749 292,298,305,308,312,313,351,353,358,366,370,373,383,388,403,413,415,428,440,444,483,495,498
%N A327749 Natural numbers whose sum of prime factors (with repetition) is palindromic in base 10.
%C A327749 Union of 1, A046352 and the palindromic primes (A002385). - Corrected by _Robert Israel_, Nov 20 2020
%D A327749 Karl G. Kröber, "Palindrome, Perioden und Chaoten: 66 Streifzüge durch die palindromischen Gefilde" (1997, Deutsch-Taschenbücher; Bd. 99) ISBN 3-8171-1522-9.
%D A327749 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 71.
%H A327749 Robert Israel, <a href="/A327749/b327749.txt">Table of n, a(n) for n = 1..10000</a>
%p A327749 ispali:= proc(n) option remember; local L; L:= convert(n,base,10); evalb(L = ListTools:-Reverse(L)) end proc:
%p A327749 spf:= proc(n) add(t[1]*t[2],t=ifactors(n)[2]) end proc:
%p A327749 select(t -> ispali(spf(t)), [$0..1000]); # _Robert Israel_, Nov 20 2020
%t A327749 sopfr[1] = 0; sopfr[n_] := Plus @@ (Times @@@ FactorInteger[n]); aQ[n_] := PalindromeQ[sopfr[n]]; Select[Range[500], aQ] (* _Amiram Eldar_, Sep 23 2019 *)
%o A327749 (PARI) sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
%o A327749 isok(n) = my(d=digits(sopfr(n))); d == Vecrev(d); \\ _Michel Marcus_, Sep 27 2019
%o A327749 (Magma) [1] cat [k: k in [2..500]| Intseq(a) eq Reverse(Intseq(a)) where a is &+[m[1]*m[2]: m in Factorization(k)]]; // _Marius A. Burtea_, Sep 27 2019
%Y A327749 Cf. A001414, A002113, A002385, A046352, A046355.
%K A327749 nonn,base
%O A327749 1,2
%A A327749 _Robert Bilinski_, Sep 23 2019