A113457 -id:A113457 - cp's OEIS frontend

A113456 Square array read by antidiagonals: a(n, d) is the smallest number that begins an arithmetic progression with common difference d of n numbers with the same prime signature.

1, 2, 1, 33, 3, 1, 19940, 3, 2, 1, 204323, 213, 155, 3, 1, 380480345, 213, 7572, 3, 2, 1

Offset: 1

David Wasserman, Jan 08 2006; corrected Jan 08 2006

First two columns are A034173 and A113457. First three rows are A000012, A086489 and A113458.

			a(3, 2) = 3 because 3, 5 and 7 have the same prime signature.

A113466 Least number that begins an n-term arithmetic progression with common difference 2 in which all terms have the same number of divisors.

Original entry on oeis.org

1, 3, 3, 213, 213, 1383, 3091, 8129, 943607, 943607, 19235031, 21470685, 21470685, 21470685, 21470685

Offset: 1

David Wasserman, Jan 08 2006

Second column of A113465. Next term is > 6368300000.

			a(4) = 213 because 213, 215, 217 and 219 each have 4 divisors.

Cf. A113457, A113465.

Module[{nn=21470695,ds},ds=Table[DivisorSigma[0,n],{n,1,nn,2}];2*Table[ SequencePosition[ds,PadRight[{},k,x_],1],{k,15}][[All,1]]][[All,1]]-1 (* Requires Mathematica version 10 or later *) (* The program will take a long time to run. To generate the first 8 terms of the sequence, change the nn constant to 8200 and the k range from 15 to 8 and the program will run quickly. *) (* Harvey P. Dale, Aug 16 2020 *)

cp's OEIS Frontend

A113456 Square array read by antidiagonals: a(n, d) is the smallest number that begins an arithmetic progression with common difference d of n numbers with the same prime signature.

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A113466 Least number that begins an n-term arithmetic progression with common difference 2 in which all terms have the same number of divisors.

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Mathematica