A026478 a(n) = least positive integer > a(n-1) and not of form a(i)*a(j)*a(k) for 1<=i<=j<=k

1, 2, 3, 5, 7, 11, 13, 16, 17, 19, 23, 24, 29, 31, 36, 37, 40, 41, 43, 47, 53, 54, 56, 59, 60, 61, 67, 71, 73, 79, 81, 83, 84, 88, 89, 90, 97, 100, 101, 103, 104, 107, 109, 113, 126, 127, 128, 131, 132, 135, 136, 137, 139, 140, 149, 150, 151, 152, 156, 157, 163, 167

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Number of repeated prime divisors of a(n) is a square for a(n) < 128. - Jason Earls, Jul 01 2001

Numbers a(n) such that A001222(a(n)) is not a square are 128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832, 972, ... - Altug Alkan, Sep 26 2016

Examples

			13 is an obvious term because it is a prime.
15 is not a term because it is a semiprime; 15 = a(1)*a(3)*a(4) = 1*3*5.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001222, A016777.

There are six related sequences: A026477: 1 <= i < j < k < n starting 1,2,3; A026478: 1 <= i <= j <= k < n starting 1,2,3; A026479: 1 <= i < j < k < n starting 1,2,4; A026480: 1 <= i <= j <= k < n starting 1,2,4; A026481: 1 <= i < j < k < n starting 1,3,4; A026482: 1 <= i <= j <= k < n starting 1,3,4.

Programs

PARI

print1(1, ", "); for(n=1, 1e3, if(bigomega(n) % 3 == 1, print1(n, ", "))); \\ Altug Alkan, Sep 26 2016

Formula

1 together with numbers with 3m+1 prime factors (for some m >= 0).

Extensions

Formula from Henry Bottomley, Feb 09 2000

Definition corrected by and more terms from Larry Reeves (larryr(AT)acm.org), Mar 24 2000

Terms corrected (128 removed) by Charles R Greathouse IV, Aug 25 2016

As pointed out by Don Reble, 128 IS a member of this sequence. - N. J. A. Sloane, Sep 23 2016