A136410 Numbers k having a proper divisor d > 2 such that d-1 divides k-1.

9, 15, 16, 21, 25, 27, 28, 33, 36, 39, 40, 45, 49, 51, 52, 57, 63, 64, 65, 66, 69, 75, 76, 81, 85, 87, 88, 91, 93, 96, 99, 100, 105, 111, 112, 117, 120, 121, 123, 124, 125, 126, 129, 133, 135, 136, 141, 144, 145, 147, 148

Offset

1,1

Comments

There is a triangular array of n dots, having at least three rows, having row sizes 1, 1+2x, 1+4x, 1+6x, ... iff n is in this sequence (where x equals all the natural numbers). - Peter Woodward, Apr 24 2015

The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 1, 32, 381, 3929, 39703, 398182, 3985220, 39863899, 398676976, 3986887465, ... . Apparently, the asymptotic density of this sequence exists and equals 0.3986... . - Amiram Eldar, Jun 06 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

E.g., consider k = 91: we can take d = 7, 7 divides 91 and 6 divides 90, so 91 is in the sequence.

Maple

N:= 1000: # to get all terms <= N
{seq(seq(d+k*d*(d-1), k=1..floor((N-d)/d/(d-1))), d=3..floor(sqrt(N)))};
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list));  # Robert Israel, Apr 24 2015

Mathematica

fQ[n_] := Block[{d = Select[ Take[ Divisors@ n, {2, -2}], # > 2 &]}, Union[IntegerQ /@ ((n - 1)/(d - 1))][[ -1]]]; Select[ Range@ 175, !PrimeQ@ # && fQ@ # &] (* Robert G. Wilson v, May 04 2008 *)

Prog

(PARI) is(k) = fordiv(k, d, if(d > 2 && d < k && !((k-1) % (d-1)), return(1))); 0; \\ Amiram Eldar, Jun 06 2024

Crossrefs

Sequence in context: A058957 A257409 A105882 * A324879 A066942 A257048

Adjacent sequences: A136407 A136408 A136409 * A136411 A136412 A136413

Keyword

nonn

Author

J. Perry (johnandruth(AT)jrperry.orangehome.co.uk), Apr 13 2008

Extensions

Definition, terms and offset corrected by M. F. Hasler, May 01 2008

Edited by N. J. A. Sloane, May 10 2008

Status

approved