A342401 Numbers k such that the number of distinct sums of distinct unitary divisors of k sets a new record.
1, 2, 6, 10, 30, 42, 60, 66, 78, 90, 110, 130, 170, 190, 210, 330, 390, 462, 510, 546, 570, 690, 798, 858, 870, 930, 1050, 1110, 1218, 1230, 1290, 1410, 1470, 1554, 1590, 1722, 1770, 1830, 1974, 2010, 2130, 2190, 2310, 2730, 3570, 3990, 4290, 4830, 5610, 6006
Offset: 1
Keywords
Examples
The first 6 terms of A342400 are 1, 3, 3, 3, 3 and 12. The record values, 1, 3 and 12, occur are 1, 2 and 6, the first 3 terms of this sequence.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..99
- Amiram Eldar, Table of n, a(n), A342400(a(n)) for n = 1..99
Programs
-
Mathematica
f[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &], x, s, m, c}, m = Length[d]; s = Plus @@ d; c = Rest @ CoefficientList[Series[Product[1 + x^d[[i]], {i, 1, m}], {x, 0, s}], x]; Count[c, _?(# > 0 &)]]; fmax = -1; seq = {}; Do[f1 = f[n]; If[f1 > fmax, fmax = f1; AppendTo[seq, n]], {n, 1, 10^3}]; seq
Comments