A242068 First of two consecutive sphenic numbers with no semiprime between them.

102, 170, 230, 238, 255, 282, 285, 366, 399, 429, 430, 434, 438, 598, 602, 606, 609, 615, 638, 642, 645, 651, 663, 741, 759, 805, 822, 826, 854, 902, 935, 969, 986, 1001, 1022, 1030, 1065, 1085, 1086, 1102, 1105, 1130, 1178, 1182, 1221, 1245, 1265, 1295, 1309, 1310, 1334, 1358, 1374, 1406, 1419, 1426, 1434

Offset

1,1

Comments

Sphenic numbers are products of three distinct primes. Semiprimes are products of two primes, not necessarily distinct.

Contains A215217.

Links

Robert Israel, Table of n, a(n) for n = 1..8683

Example

102=2*3*17 and 105=3*5*7 are sphenic numbers, i.e., products of three distinct primes, and neither 103 (a prime) nor 104=2^3*13 is a semiprime, so 102 is in the sequence.

Maple

N:= 10000: # to get all terms where the next sphenic number <= N
Sphenics:= select(t -> (map(s->s[2], ifactors(t)[2])=[1, 1, 1]), {$1..N}):
Primes:= select(isprime, {2, seq(2*i+1, i=1..floor(N/2))}):
Semiprimes:= {seq(seq(p*q, q=select(`<=`, Primes, N/p)), p=Primes)}:
map(proc(i) if nops(Semiprimes intersect {$Sphenics[i]..Sphenics[i+1]}) = 0 then Sphenics[i] else NULL fi end proc, [$1..nops(Sphenics)-1]);

Mathematica

sw = Switch[FactorInteger[#][[All, 2]], {1, 1}, {#, 2}, {1, 1, 1}, {#, 3}, _, Nothing]& /@ Range[10^4];
sp = SequencePosition[sw, {{_, 3}, {_, 3}}][[All, 1]];
sw[[sp]][[All, 1]] (* Jean-François Alcover, Sep 26 2020 *)

Crossrefs

Cf. A001358, A007304, A215217.

Sequence in context: A145578 A318792 A006316 * A053326 A151955 A244387

Adjacent sequences: A242065 A242066 A242067 * A242069 A242070 A242071

Keyword

nonn

Author

Robert Israel, Aug 13 2014

Status

approved