A392783 Non-palindromic numbers whose digit reversal have the same sum of distinct prime factors.

120, 360, 1089, 1131, 1200, 1311, 1320, 1440, 2178, 2262, 2622, 2675, 3393, 3600, 3933, 3960, 4154, 4356, 4514, 4636, 5762, 6364, 6534, 8712, 8749, 9478, 9801, 10989, 12000, 12120, 12441, 13200, 13320, 14269, 14400, 14421, 14520, 15167, 15602, 15720, 15840, 16237

Offset

1,1

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Example

360 is a term as 360 = 2^3*3^2*5 that has a sum of distinct prime factors of 2+3+5 = 10, while the digit reversal of 360 is 63 = 3^2*7 that has a sum of distinct prime factors of 3+7 = 10.

Mathematica

q[k_]:=!PalindromeQ[k]&&Total[First/@FactorInteger[k]]==Total[First/@FactorInteger[IntegerReverse[k]]]; Select[Range[16237], q] (* James C. McMahon, Mar 05 2026 *)

Prog

(PARI) sopf(n) = my(fac=factor(n)); sum(i=1, matsize(fac)[1], fac[i, 1]); \\ A008472
isok(k) = my(d=digits(k)); if (d != Vecrev(d), sopf(k) == sopf(fromdigits(Vecrev(d)))); \\ Michel Marcus, Mar 05 2026
(Python)
from sympy import factorint
def sopf(n): return sum(factorint(n))
def ok(n): return n != (r:=int(str(n)[::-1])) and sopf(n) == sopf(r)
print([k for k in range(20000) if ok(k)]) # Michael S. Branicky, Mar 05 2026

Crossrefs

Cf. A004086, A008472, A029742, A085607, A115662.

Sequence in context: A144524 A052768 A242845 * A234915 A061218 A321841

Adjacent sequences: A392780 A392781 A392782 * A392784 A392785 A392786

Keyword

nonn,base

Author

Scott R. Shannon, Mar 05 2026

Status

approved