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

1,2

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A338883 A055722 A028830 * A171828 A379594 A246450

Adjacent sequences: A327746 A327747 A327748 * A327750 A327751 A327752

Keyword

nonn,base

Author

Robert Bilinski, Sep 23 2019

Status

approved