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

1,1

Comments

Also called the one-sided numbers.

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

VOS 2025 Math Region stage, Problem 10.9 (in Russian).

Example

39 = 3*13.

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 *)

Prog

(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

Crossrefs

Cf. A004615.

Sequence in context: A165461 A020166 A393978 * A046448 A249701 A039467

Adjacent sequences: A380755 A380756 A380757 * A380759 A380760 A380761

Keyword

nonn,base

Author

Yaroslav Deryavko, Feb 01 2025

Status

approved