A175502 -id:A175502 - cp's OEIS frontend

A175503 a(n) = the number of divisors of A175502(n).

1, 2, 2, 3, 4, 2, 6, 4, 4, 5, 2, 8, 3, 6, 6, 8, 4, 9, 2, 10, 4, 12, 2, 7, 4, 16, 2, 15, 4, 18, 2, 14, 3, 3, 12, 6, 10, 8, 8, 5, 6, 9, 8, 12, 12, 10, 3, 16, 6, 20, 2, 24, 4, 14, 6, 18, 8, 16, 12, 9, 10, 10, 16, 9, 3, 18, 12, 15, 6, 24, 8, 20, 4, 21, 2, 30, 4, 32, 2, 27

Offset: 1

Leroy Quet, May 31 2010

nonn

Each unordered pair {a(k),a(k-1)} occurs at most once in the sequence.

Ivan Neretin, Table of n, a(n) for n = 1..1000

Cf. A175502

More terms from Ivan Neretin, Jun 05 2016

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.

Original entry on oeis.org

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

Leroy Quet, May 31 2010

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

Paul Tek, Table of n, a(n) for n = 1..2473
Paul Tek, C++ program for this sequence

Cf. A175501, A175502

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

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

cp's OEIS Frontend

A175503 a(n) = the number of divisors of A175502(n).

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