A038456 List of pairs of consecutive numbers each with 4 divisors (duplicates removed).

14, 15, 21, 22, 26, 27, 33, 34, 35, 38, 39, 57, 58, 85, 86, 87, 93, 94, 95, 118, 119, 122, 123, 133, 134, 141, 142, 143, 145, 146, 158, 159, 177, 178, 201, 202, 203, 205, 206, 213, 214, 215, 217, 218, 219, 253, 254, 298, 299, 301, 302, 303, 326, 327, 334, 335, 381, 382, 393, 394, 395, 445, 446, 447, 453, 454

Offset: 1

Author

Felice Russo

Keywords

• nonn

Examples

			14 and 15 because both have 4 as number of divisors and are consecutive.
		

References

• D. Wells, Curious and interesting numbers, Penguin Books.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A039832, A039833.

Programs

Mathematica

Union[Flatten[Select[Partition[Range[500],2,1],DivisorSigma[0,First[#]] == DivisorSigma[0,Last[#]]==4&]]] (* Harvey P. Dale, Jul 22 2012 *)
SequencePosition[DivisorSigma[0,Range[500]],{4,4}]//Flatten//Union (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 15 2016 *)

PARI

isA038456(n) = (numdiv(n)==4) && ((numdiv(n+1)==4) || (numdiv(n-1)==4)) \\ Michael B. Porter, Feb 03 2010

Extensions

Corrected and extended by Olivier Gérard

Corrected by Rick L. Shepherd, Jun 07 2002