A046352 -id:A046352 - cp's OEIS frontend

A046353 Odd composite numbers whose sum of prime factors is palindromic (counted with multiplicity).

9, 15, 27, 45, 57, 85, 121, 123, 259, 305, 351, 403, 413, 415, 483, 495, 575, 597, 627, 639, 663, 687, 689, 705, 717, 735, 807, 875, 893, 931, 935, 985, 989, 1073, 1135, 1183, 1203, 1207, 1263, 1285, 1293, 1331, 1353, 1383, 1385, 1407, 1473, 1505, 1545

Offset: 1

Patrick De Geest, Jun 15 1998

			689 = 13 * 53 -> 13 + 53 = 66 and 66 is a palindrome.

John Cerkan, Table of n, a(n) for n = 1..10000

Cf. A046352, A046354.

palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[9,1545,2],!PrimeQ[#]&&palQ[Total[Times@@@FactorInteger[#]]]&] (* Jayanta Basu, Jun 05 2013 *)

from sympy import factorint
def is_046353(n):
    if n % 2 == 0: return False
    f = factorint(n)
    if sum([f[i] for i in f]) < 2: return False
    sfa = sum([i*f[i] for i in f])
    if sfa == int(str(sfa)[::-1]): return True
    return False # John Cerkan, Apr 24 2018

Name clarified and offset changed by John Cerkan, Apr 24 2018

A046354 Composite palindromes whose sum of prime factors is palindromic (counted with multiplicity).

Original entry on oeis.org

4, 6, 8, 9, 121, 292, 444, 575, 717, 828, 989, 1331, 2002, 4884, 5445, 8668, 9559, 10201, 11211, 11811, 13231, 14241, 14541, 14641, 15251, 15751, 16261, 16761, 18281, 19291, 19591, 20002, 21112, 21312, 22022, 22922, 23832, 26062, 26162

Offset: 1

Patrick De Geest, Jun 15 1998

			15751 = 19 * 829 -> 19 + 829 = 848 and 848 is a palindrome.

R. J. Mathar and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 681 terms from R. J. Mathar)

Cf. A046352, A046353.

n := 1 ;
for i from 3 to 30000 do
    pal := A002113(i) ;
    if not isprime(pal) then
        sof := A001414(pal) ;
        if isA002113(sof) then
            printf("%d %d\n",n,pal) ;
            n := n+1 ;
        end if;
    end if;
end do: # R. J. Mathar, Sep 09 2015

palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[4,26170],!PrimeQ[#]&&And@@palQ/@{#,Total[Times@@@FactorInteger[#]]}&](* Jayanta Basu, Jun 05 2013 *)

A046352 INTERSECT A002113. - R. J. Mathar, Sep 09 2015

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

Original entry on oeis.org

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, 85, 101, 102, 106, 116, 121, 123, 131, 151, 181, 182, 191, 194, 218, 259, 260, 278, 292, 298, 305, 308, 312, 313, 351, 353, 358, 366, 370, 373, 383, 388, 403, 413, 415, 428, 440, 444, 483, 495, 498

Offset: 1

Robert Bilinski, Sep 23 2019

Union of 1, A046352 and the palindromic primes (A002385). - Corrected by Robert Israel, Nov 20 2020

Karl G. Kröber, "Palindrome, Perioden und Chaoten: 66 Streifzüge durch die palindromischen Gefilde" (1997, Deutsch-Taschenbücher; Bd. 99) ISBN 3-8171-1522-9.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 71.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001414, A002113, A002385, A046352, A046355.

[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

ispali:= proc(n) option remember; local L; L:= convert(n,base,10); evalb(L = ListTools:-Reverse(L)) end proc:
spf:= proc(n) add(t[1]*t[2],t=ifactors(n)[2]) end proc:
select(t -> ispali(spf(t)), [$0..1000]); # Robert Israel, Nov 20 2020

sopfr[1] = 0; sopfr[n_] := Plus @@ (Times @@@ FactorInteger[n]); aQ[n_] := PalindromeQ[sopfr[n]]; Select[Range[500], aQ] (* Amiram Eldar, Sep 23 2019 *)

sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
isok(n) = my(d=digits(sopfr(n))); d == Vecrev(d); \\ Michel Marcus, Sep 27 2019

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A046353 Odd composite numbers whose sum of prime factors is palindromic (counted with multiplicity).

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A046354 Composite palindromes whose sum of prime factors is palindromic (counted with multiplicity).

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

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