A046358 Composite numbers divisible by the palindromic sum of their prime factors (counted with multiplicity).

4, 16, 27, 308, 440, 528, 594, 627, 1122, 1276, 3432, 3861, 4070, 4543, 5445, 5808, 6248, 6534, 7881, 8085, 8096, 9108, 9306, 9702, 11550, 13860, 14784, 16500, 16632, 17556, 18711, 19800, 19866, 20900, 21091, 21120, 22275, 22308, 23463, 23474

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Example

1122 = 2 * 3 * 11 * 17 -> Sum of factors is palindrome 33 -> 1122 / 33 = 34 exactly.

Maple

revdigs:= proc(n) local L, nL; L:= convert(n, base, 10); nL:= nops(L); add(L[i]*10^(nL-i), i=1..nL) end proc:
filter:= proc(n) local f;
if n = 1 or isprime(n) then return false fi;
f:= add(t[1]*t[2], t=ifactors(n)[2]);
f = revdigs(f) and n mod f = 0
end proc:
select(filter, [$1..24000]); # Robert Israel, Aug 12 2014

Mathematica

palQ[n_]:= Reverse[x=IntegerDigits[n]] == x; Select[Range[4, 23480], !PrimeQ[#] && palQ[y=Total[Times@@@FactorInteger[#]]] && IntegerQ[#/y]&](* Jayanta Basu, Jun 05 2013 *)

Prog

(Python)
from sympy import isprime, factorint
A046358 = [n for n in range(2, 10**6) if not isprime(n) and not n % sum([p*e for p, e in factorint(n).items()]) and str(sum([p*e for p, e in factorint(n).items()])) == str(sum([p*e for p, e in factorint(n).items()]))[::-1]] # Chai Wah Wu, Aug 12 2014
(PARI)
rev(n)=my(r=""); d=digits(n); for(i=1, #d, r=concat(Str(d[i]), r)); return(eval(r))
sumfact(n)=my(v=Vec(factor(n))); p=0; for(j=1, #v[1], p+=v[1][j]*v[2][j]); return(p)
forcomposite(n=1, 10^5, if(rev(sumfact(n))==sumfact(n)&&n%sumfact(n)==0, print1(n, ", "))) \\ Derek Orr, Aug 12 2014

Crossrefs

Cf. A046359, A046360.

Sequence in context: A097374 A257309 A271936 * A046366 A227609 A219338

Adjacent sequences: A046355 A046356 A046357 * A046359 A046360 A046361

Keyword

nonn,base

Author

Patrick De Geest, Jun 15 1998

Extensions

Definition, offset and a(24) corrected by Chai Wah Wu, Aug 12 2014

Status

approved