A331194 Numbers whose last digit is the number of their distinct prime factors.

11, 12, 22, 31, 41, 52, 61, 62, 71, 72, 81, 82, 92, 101, 112, 121, 122, 131, 142, 151, 152, 162, 172, 181, 191, 192, 202, 211, 212, 232, 241, 242, 251, 262, 271, 272, 273, 281, 292, 302, 311, 331, 332, 352, 361, 362, 382, 392, 401, 412, 421, 422, 431, 432, 452

Offset

1,1

Comments

All prime numbers whose last digit is 1 have this property.

Only numbers with at most 9 distinct prime factors appear in this sequence.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

272 is such a number because 272 = 2^4 * 17. It has 2 distinct prime factors {2,17} and its last digit is 2.

Mathematica

Select[Range@500, Last@IntegerDigits@#==PrimeNu@#&]
Select[Range[500], PrimeNu[#]==NumberDigit[#, 0]&] (* Harvey P. Dale, Aug 12 2021 *)

Prog

(PARI) isok(m) = omega(m) == (m % 10); \\ Michel Marcus, Feb 24 2020
(Python)
from sympy import factorint
def ok(n): return n > 1 and n%10 == len(factorint(n))
print([k for k in range(460) if ok(k)]) # Michael S. Branicky, Nov 12 2021

Crossrefs

Cf. A001221 (omega), A010879 (final digit of n).

Sequence in context: A118512 A112651 A215027 * A105945 A139114 A367556

Adjacent sequences: A331191 A331192 A331193 * A331195 A331196 A331197

Keyword

nonn,base

Author

Giorgos Kalogeropoulos, Feb 23 2020

Extensions

a(49) and beyond from Michael S. Branicky, Nov 12 2021

Status

approved