A108728 -id:A108728 - cp's OEIS frontend

A019520 a(n) is the concatenation of the first n positive even numbers.

2, 24, 246, 2468, 246810, 24681012, 2468101214, 246810121416, 24681012141618, 2468101214161820, 246810121416182022, 24681012141618202224, 2468101214161820222426, 246810121416182022242628, 24681012141618202224262830, 2468101214161820222426283032

Offset: 1

R. Muller

H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.
F. Smarandache, "Collected Papers", Vol. II, Tempus Publ. Hse., Bucharest, Romania, 1996.
S. Smarandoiu, Convergence of Smarandache continued fractions, Abstract 96T-11-195, Abstracts Amer. Math. Soc., 17 (No. 4, 1996), 680.

Eric Weisstein's World of Mathematics, Consecutive Number Sequences

Cf. A019519 (similar, with odd numbers), A067095, A108728.

Table[FromDigits[Flatten[IntegerDigits/@(2Range[n])]],{n,20}] (* Harvey P. Dale, Mar 24 2013 *)

def a(n): return int("".join(str(2*i) for i in range(1, n+1)))
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Dec 18 2021

Lim_{n->oo} A019519(n)/a(n) = 0 (see A067095). - Bernard Schott, Dec 18 2021

More terms from Erich Friedman

More terms from Harvey P. Dale, Mar 24 2013

A105388 Number of divisors of concatenated even numbers.

Original entry on oeis.org

2, 8, 8, 6, 32, 12, 4, 48, 96, 48, 8, 40, 64, 24, 32, 32, 12, 96, 16, 448, 64, 48, 256, 16, 192, 36, 24, 640, 32, 192, 16, 32, 256, 72, 256, 288, 16, 384, 256, 256, 32, 12, 128, 60, 160, 1536, 2048, 64, 16, 2304, 64, 64, 96, 72, 32, 48, 512, 24, 256, 1536, 64, 72, 768, 40, 4096, 48, 16, 512, 1024, 48, 1024

Offset: 1

Parthasarathy Nambi, Apr 30 2005

			The number of divisors of 24 is 8 - which is the second term.
The number of divisors of 246 is 8 - which is the third term.
The number of divisors of 2468 is 6 - which is the fourth term.

Max Alekseyev, Table of n, a(n) for n = 1..90 (terms 88..89 from Tyler Busby).

Cf. A019520, A108728 (number of distinct prime divisors).

Table[DivisorSigma[0,FromDigits[Flatten[IntegerDigits/@(2Range[n])]]],{n,30}] (* Harvey P. Dale, Dec 10 2016 *)

More terms from Harvey P. Dale, Dec 10 2016
a(30)-a(69) from Michael S. Branicky, Feb 08 2021 (computed using prime factorizations linked in A108728)
Offset corrected and a(70)-a(71) added by Max Alekseyev, Mar 21 2023

cp's OEIS Frontend

A019520 a(n) is the concatenation of the first n positive even numbers.

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