login
A325161
Nonprime squarefree numbers not divisible by any two consecutive primes.
9
1, 10, 14, 21, 22, 26, 33, 34, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 91, 93, 94, 95, 106, 110, 111, 115, 118, 119, 122, 123, 129, 130, 133, 134, 141, 142, 145, 146, 155, 158, 159, 161, 166, 170, 177, 178, 182, 183, 185, 187, 190, 194, 201
OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of non-singleton integer partitions into distinct non-consecutive parts (counted by A003114 minus 1).
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
10: {1,3}
14: {1,4}
21: {2,4}
22: {1,5}
26: {1,6}
33: {2,5}
34: {1,7}
38: {1,8}
39: {2,6}
46: {1,9}
51: {2,7}
55: {3,5}
57: {2,8}
58: {1,10}
62: {1,11}
65: {3,6}
69: {2,9}
74: {1,12}
82: {1,13}
MATHEMATICA
Select[Range[100], !PrimeQ[#]&&Min@@Differences[Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]>1&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 05 2019
STATUS
approved