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

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

Author

Robert Bilinski, Sep 23 2019

Keywords

• nonn
• base

Comments

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

References

• 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.

Links

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

Crossrefs

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

Programs

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

Maple

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

Mathematica

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

PARI

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