A160690 a(1)=1. a(n) = the smallest integer > a(n-1) such that d(a(n)) = d(a(n) - a(n-1)), where d(m) = the number of divisors of m.

1, 3, 5, 7, 15, 17, 19, 27, 29, 31, 39, 41, 43, 51, 53, 74, 79, 85, 91, 106, 109, 115, 123, 129, 131, 141, 153, 159, 171, 173, 183, 205, 213, 219, 253, 259, 265, 287, 295, 301, 309, 311, 313, 319, 327, 335, 337, 343, 358, 389, 395, 397, 403, 411, 417, 419, 421

Offset

1,2

Comments

a(n) - A160690(n-1) = A160689(n), for n >= 2.

d(A160689(n)) = d(a(n)) = A160691(n).

Links

Michel Marcus, Table of n, a(n) for n = 1..5000

Mathematica

a[1] = 1; a[n_] := a[n] = (For[m = a[n - 1] + 1, DivisorSigma[0, m] != DivisorSigma[0, m - a[n - 1]], m++]; m); Table[a[n], {n, 57}] (* Farideh Firoozbakht, May 28 2009 *)

Prog

(PARI) lista(nn) = {k = 1; print1(k, ", "); last = k; for (n=2, nn, k = last+1; while(numdiv(k) != numdiv(k - last), k++); print1(k, ", "); s += k; last = k; ); } \\ Michel Marcus, Sep 05 2017

Crossrefs

Cf. A160689, A160691.

Sequence in context: A341845 A073692 A132012 * A085494 A348441 A356591

Adjacent sequences: A160687 A160688 A160689 * A160691 A160692 A160693

Keyword

nonn

Author

Leroy Quet, May 24 2009

Extensions

More terms from Farideh Firoozbakht, May 28 2009

Status

approved