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A175500 a(1) = 1. a(n) = the smallest integer not yet occurring such that if d(a(n)) = d(a(k)), then d(a(n-1)) doesn't equal d(a(k-1)) for any k where 2<= k <= n-1, where d(m) = the number of divisors of m. 5
1, 2, 3, 4, 5, 6, 7, 12, 8, 9, 10, 14, 16, 11, 24, 13, 36, 15, 18, 17, 48, 19, 60, 20, 25, 28, 30, 21, 40, 32, 44, 64, 22, 72, 23, 81, 26, 80, 27, 100, 29, 120, 31, 144, 33, 168, 34, 180, 35, 192, 37, 240, 38, 324, 41, 252, 42, 49, 54, 56, 84, 39, 336, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is a permutation of the positive integers.

The derived sequence 2^d(a(n))*3^d(a(n+1)), where d(m) = the number of divisors of m, contains only distinct terms. - Paul Tek, Mar 05 2014

LINKS

Paul Tek, Table of n, a(n) for n = 1..2473

Paul Tek, C++ program for this sequence

PROG

(PARI) ok(j, va, vs, n) = {if (vecsearch(vs, j), return (0)); for (k=1, n-1, if ((numdiv(j) == numdiv(va[k])) && (numdiv(va[k-1]) == numdiv(va[n-1])), return (0)); ); 1; }

findnew(va, vs, n) = {my(j = 1); my(vs = vecsort(va)); until (ok(j, va, vs, n), j++); j; }

lista(nn) = {my(va = [1]); for (n=2, nn, vs = vecsort(va); newa = findnew(va, vs, n); va = concat(va, newa); ); va; } \\ Michel Marcus, May 04 2016

CROSSREFS

Cf. A175501, A175502

Sequence in context: A271835 A118599 A178531 * A222259 A243575 A284447

Adjacent sequences:  A175497 A175498 A175499 * A175501 A175502 A175503

KEYWORD

nonn,look

AUTHOR

Leroy Quet, May 31 2010

EXTENSIONS

a(26)-a(64) from Paul Tek, Mar 05 2014

STATUS

approved

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)