A272600 Composites k such that p-1 divides k-1 for each prime divisor of k-1.

9, 21, 25, 33, 49, 55, 65, 81, 85, 121, 129, 145, 161, 169, 201, 217, 221, 253, 273, 289, 295, 301, 321, 325, 343, 361, 385, 441, 469, 481, 501, 505, 513, 545, 589, 625, 649, 685, 721, 781, 801, 817, 841, 865, 901, 961, 973, 1001, 1025, 1027, 1081, 1089, 1101, 1135, 1177, 1261, 1281, 1333, 1345, 1369, 1405, 1441, 1501

Offset

1,1

Comments

Composites not in A272601.

Links

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

Mathematica

pdkQ[n_]:=Module[{p=FactorInteger[n-1][[;; , 1]]-1}, AllTrue[(n-1)/p, IntegerQ]]; Select[Range[ 1550], CompositeQ[#]&&pdkQ[#]&] (* Harvey P. Dale, Feb 26 2024 *)

Prog

(PARI) forcomposite(n=4, 10^4, my(q=1, f=factor(n-1)[, 1]); for(j=1, #f, if((n-1)%(f[j]-1), q=0; break)); if(q, print1(n, ", ") ) );
(PARI) is(n)=my(f=factor(n-1)[, 1]); for(i=1, #f, if((n-1)%(f[i]-1), return(0))); !isprime(n) && n>1 \\ Charles R Greathouse IV, May 16 2016

Crossrefs

Cf. A080062 (composite n such that p-1 divides n-1 for each prime divisor of n).

Sequence in context: A143791 A091113 A188159 * A359161 A327862 A108181

Adjacent sequences: A272597 A272598 A272599 * A272601 A272602 A272603

Keyword

nonn

Author

Joerg Arndt, May 16 2016

Status

approved