A356766 Least number k such that k and k+2 both have exactly 2n divisors, or -1 if no such number exists.

3, 6, 18, 40, 127251, 198, 26890623, 918, 17298, 6640, 25269208984375, 3400, 3900566650390623, 640062, 8418573, 18088, 1164385682220458984373, 41650, 69528379848480224609373, 128464, 34084859373, 12164094, 150509919493198394775390625, 90270, 418514293125, 64505245696

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Example

For n=1, numdiv(3) = numdiv(5) = 2 = 2*1, and no number < 3 satisfies this, hence a(1) = 3.

Mathematica

a={}; n=1; nmax=10; For[k=1, n<=nmax, k++, If[DivisorSigma[0, k] == DivisorSigma[0, k+2] == 2n, AppendTo[a, k]; k=1; n++]]; a (* Stefano Spezia, Aug 26 2022 *)
Flatten[Table[SequencePosition[DivisorSigma[0, Range[27*10^6]], {2n, _, 2n}, 1], {n, 10}], 1][[;; , 1]] (* The program generates the first 10 terms of the sequence. To generate more, increase the Range constant but the program will take a long time to run. *) (* Harvey P. Dale, Jul 01 2023 *)

Prog

(PARI) a(n)=for(k=1, +oo, if(numdiv(k)==2*n&&numdiv(k+2)==2*n, return(k)))

Crossrefs

Numbers k such that k and k+2 both have exactly m divisors: A001359 (m=2), A356742 (m=4), A356743 (m=6), A356744 (m=8).

Cf. A000005 (d(n)), A003680, A005238, A006558, A006601, A062832, A067888, A067889, A075036.

Sequence in context: A081150 A362014 A216813 * A181037 A222856 A342583

Adjacent sequences: A356763 A356764 A356765 * A356767 A356768 A356769

Keyword

nonn

Author

Jean-Marc Rebert, Aug 26 2022

Extensions

More terms from Jinyuan Wang, Aug 28 2022

Status

approved