A175590 Numbers k with prime signature(k) = prime signature(k+1) = prime signature(k+2) = prime signature(k+3).

19940, 49147, 54585, 118923, 136825, 183554, 204323, 204324, 262932, 304675, 361275, 361322, 476377, 486962, 506905, 619722, 668211, 734948, 854018, 937025, 938203, 999649, 1062025, 1118275, 1335572, 1336075, 1356324, 1466225, 1541491

Offset: 1

Author

Charles R Greathouse IV, Jul 19 2010

Keywords

• nonn

Examples

			a(1) = 2^2 * 5 * 997; a(1)+1 = 3 * 17^2 * 23; a(1)+2 = 2 * 13^2 * 59; a(1)+3 = 7^2 * 11 * 37. All have prime signature {2, 1, 1}.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052213, A052214, A218448. Subsequence of A070284.

Programs

Mathematica

SequencePosition[Table[Sort[FactorInteger[n][[All,2]]],{n,1542000}],{x_,x_,x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* The program will take a long time to run. *) (* Harvey P. Dale, Jun 09 2021 *)

PARI

sig(n)={vecsort(factor(n)[,2])}; s=sig(1);for(n=1,1e6,t=sig(n+1);if(s==t&t==sig(n+2)&t==sig(n+3),print1(n-1,","));s=t)

PARI

is_A175590(n)={my(f(n)=vecsort(factor(n)[,2]),t=f(n));!for(i=1,3,f(n+i)!=t & return)}  \\ M. F. Hasler, Nov 01 2012