A380758 Numbers which are not prime powers and their prime factors share a last digit in base 10.

39, 69, 117, 119, 129, 159, 207, 219, 249, 259, 299, 309, 329, 339, 341, 351, 387, 451, 469, 477, 489, 507, 519, 551, 559, 579, 621, 629, 657, 669, 671, 679, 689, 699, 747, 749, 781, 789, 799, 833, 849, 879, 889, 897, 927, 939, 949, 959, 989, 1017, 1053, 1059

Offset: 1

Author

Yaroslav Deryavko, Feb 01 2025

Keywords

• nonn
• base

Comments

Also called the one-sided numbers.

They can end only in either 1, 3, 7 or 9.

Examples

			39 = 3*13.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• VOS 2025 Math Region stage, Problem 10.9 (in Russian).

Crossrefs

Cf. A004615.

Programs

Maple

q:= n-> (l-> nops(l)>1 and nops({map(i-> irem(i[1], 10), l)[]})=1)(ifactors(n)[2]):
select(q, [$1..2000])[];  # Alois P. Heinz, Feb 18 2025

Mathematica

Sort[Times@@@Cases[Subsets[Prime[Range[100]],{2}],?(Mod[#[[1]]-#[[2]],10]==0&)]][[;;100]] (* _Shenghui Yang, Feb 18 2025 *)

PARI

isok(k) = my(f=factor(k)); (#f~ != 1) && (#Set(vector(#f~, i, f[i,1] % 10)) == 1); \\ Michel Marcus, Feb 18 2025

Python

from sympy import factorint
def ok(n): return len(f:=factorint(n)) > 1 and len(set(p%10 for p in f)) == 1
print([k for k in range(1, 1060) if ok(k)]) # Michael S. Branicky, Feb 18 2025