A072607 If D[n] is divisor-set of n, then in set of 1+D only 2 primes occur:{2,3}; also n is not squarefree.

98, 338, 578, 686, 722, 1274, 1862, 1922, 2366, 2738, 3038, 3626, 3698, 4214, 4394, 4418, 4802, 5054, 5978, 6422, 6566, 6962, 7154, 7442, 7742, 8918, 8978, 9386, 9506, 9826, 9898, 10082, 10094, 10478, 10658, 10682, 12446, 12482, 12506, 13034, 13426

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

n = 338 = 2*13*13 is not squarefree; D = {1,2,13,26,169,338}; 1 + D = {2,3,14,27,170,339} contains only two primes {2,3}. Such numbers are nonsquarefree even nontotient numbers (from A005277), present also in A051222. Their odd prime divisors seem to arise from A053176.

Mathematica

di[x_] := Divisors[x] dp[x_] := Part[di[x], Flatten[Position[PrimeQ[1+di[x]], True]]]+1 Do[s=Length[dp[n]]; If[Equal[s, 2]&&Equal[MoebiusMu[n], 0], Print[n]], {n, 1, 25000}]

Crossrefs

Cf. A000005, A005277, A002202, A067513, A051222, A053176.

Sequence in context: A202378 A202371 A195751 * A306214 A160828 A158129

Adjacent sequences: A072604 A072605 A072606 * A072608 A072609 A072610

Keyword

nonn

Author

Labos Elemer, Jun 24 2002

Status

approved