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.

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

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: A118599 A178531 A358254 * A356253 A222259 A243575

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