A085607 Non-palindromic numbers whose digit reversal have the same sum of prime factors (with repetition).

45, 54, 250, 495, 594, 1131, 1311, 2262, 2550, 2622, 2750, 2926, 3393, 3933, 4154, 4489, 4514, 4545, 4636, 4995, 5454, 5808, 5994, 6292, 6364, 6550, 7800, 8085, 8749, 9478, 9844, 12441, 13980, 14269, 14421, 15167, 15180, 15602, 16237, 18449, 18977

Offset

1,1

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000 (1..500 from Harvey P. Dale).

Example

250 is a term because 250 = 2*5^3 and 52 = 2^2*13 and 2+5+5+5 = 2+2+13 = 17.

Mathematica

spf[n_]:=Total[Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[n]]];
spffQ[ n_]:=!PalindromeQ[n]&&spf[n]==spf[IntegerReverse[n]];
Select[Range[ 20000], spffQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 19 2017 *)

Prog

(Python)
from sympy import factorint
def sopfr(n): return sum(p*e for p, e in factorint(n).items())
def ok(n): return n != (r:=int(str(n)[::-1])) and sopfr(n) == sopfr(r)
print([k for k in range(20000) if ok(k)]) # Michael S. Branicky, Mar 05 2026

Crossrefs

Cf. A001414, A029742.

Sequence in context: A039423 A043246 A044026 * A087993 A062390 A167328

Adjacent sequences: A085604 A085605 A085606 * A085608 A085609 A085610

Keyword

base,nonn

Author

Jason Earls, Jul 08 2003

Extensions

Corrected by T. D. Noe, Oct 25 2006

Status

approved