A338628 a(n) is the smallest number k such that n consecutive integers starting at k have the same number of square divisors (A046951).

1, 1, 1, 844, 3624, 22020, 671346, 8870024, 264459172, 463239475, 1407472722, 108494875170, 12385053656370, 145065154350545

Offset

1,4

Links

Table of n, a(n) for n=1..14.

Index entries for sequences related to divisors of numbers

Example

844 has 2 square divisors {1, 4}, 845 has 2 square divisors {1, 169}, 846 has 2 square divisors {1, 9} and 847 has 2 square divisors {1, 121}. These are the first 4 consecutive numbers with the same number of square divisors, so a(4) = 844.

Mathematica

Do[find = 0; k = 0; While[find == 0, k++; If[Length[Union[Table[Length[Select[Divisors[j], IntegerQ[Sqrt[#]] &]], {j, k, k + n - 1}]]] == 1, find = 1; Print[k]]], {n, 1, 7}]

Prog

(PARI) isok(n, k) = #Set(apply(x->sumdiv(x, d, issquare(d)), vector(n, i, k+i-1))) == 1;
a(n) = my(k=1); while(! isok(n, k), k++); k; \\ Michel Marcus, Nov 05 2020

Crossrefs

Cf. A006558, A045983, A045984, A046951, A324593, A324594.

Sequence in context: A334183 A078144 A071320 * A323253 A160212 A188296

Adjacent sequences: A338625 A338626 A338627 * A338629 A338630 A338631

Keyword

nonn,more

Author

Ilya Gutkovskiy, Nov 04 2020

Extensions

a(8)-a(11) from Amiram Eldar, Nov 04 2020

a(12)-a(14) from Martin Ehrenstein, Jul 19 2023

Status

approved