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A302022 Primitive terms from A005279. 3
6, 15, 20, 28, 35, 63, 77, 88, 91, 99, 104, 110, 117, 130, 143, 153, 170, 187, 190, 209, 221, 238, 247, 266, 272, 299, 304, 322, 323, 325, 357, 368, 391, 399, 425, 437, 464, 475, 483, 493, 496, 506, 513, 527, 551, 575, 589, 609, 621, 638, 651, 667, 682, 703, 713, 725, 754, 759, 775, 777, 783, 806, 814 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also numbers k such that k is in A005279 but none of the proper divisors of k are.

All terms k are composites; if k is prime then it's not in A005279 hence not here. If k = m * t and t < m < 2*t then m and t are coprime. If g = gcd(t, m) > 1 then the integer k / g^2 is in A005279. If there is some term u*t where with u > 2*t and gcd(u, t) = 1 then there is some m * t' with gcd(m, t') = 1 such that m*t' | t * u and t * u wouldn't be in the sequence. if u = 2*t then gcd(u, t) = t which can't happen.

It could be that both m and t are composite, for example, t = 53^2 and m = 5^5 gives the term 53^2 * 5^5.

Interestingly, k = m * t where t < m < 2 * t and m * t is in A005279 and m, t coprime gives A106430; this sequence is a subsequence of A106430.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

A301989(a(n)) = 1.

EXAMPLE

77 is a term since it is in A005279 and 77 is not of the form A005279(i)*t for t > 1.

PROG

(PARI) is005279(n) = my(d=divisors(n)); for(i=3, #d, if(d[i]<2*d[i-1], return(1))); 0;

is(n) = if (is005279(n), d = divisors(n); for (k=1, #d-1, if (is005279(d[k]), return (0)); ); return(1); ); \\ Altug Alkan, Apr 14 2018

upto(n) = {my(res = List()); for(i = 2, sqrtint(n), for(j = i+1, min(2 * i - 1, n\i), if(gcd(i, j) == 1, if(is(i*j), listput(res, i*j))))); listsort(res); return(res)} \\ David A. Corneth, Apr 15 2018

CROSSREFS

Cf. A005279, A020886, A106430, A301989, A302296.

Sequence in context: A128253 A020886 A093508 * A094183 A196394 A162693

Adjacent sequences:  A302019 A302020 A302021 * A302023 A302024 A302025

KEYWORD

nonn

AUTHOR

David A. Corneth, Mar 31 2018

STATUS

approved

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Last modified May 26 11:08 EDT 2022. Contains 354086 sequences. (Running on oeis4.)