A026478 - OEIS

A026478

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

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

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OFFSET

1,2

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

LINKS

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

FORMULA

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

EXAMPLE

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.

PROG

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

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.

Sequence in context: A062063 A211338 A167175 * A211485 A154893 A084111

Adjacent sequences: A026475 A026476 A026477 * A026479 A026480 A026481

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

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

STATUS

approved