A325161 Nonprime squarefree numbers not divisible by any two consecutive primes.

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

Author

Gus Wiseman, Apr 05 2019

Keywords

• nonn

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).

Examples

			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}
		

Links

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

Crossrefs

Cf. A001227, A003114, A005117, A025157, A034296, A056239, A073485, A073491, A089995, A112798, A116931, A319630, A325160, A325162.

Programs

Mathematica

Select[Range[100],!PrimeQ[#]&&Min@@Differences[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]>1&]