cp's OEIS Frontend

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

%I A325161 #9 Jan 09 2021 04:44:25
%S A325161 1,10,14,21,22,26,33,34,38,39,46,51,55,57,58,62,65,69,74,82,85,86,87,
%T A325161 91,93,94,95,106,110,111,115,118,119,122,123,129,130,133,134,141,142,
%U A325161 145,146,155,158,159,161,166,170,177,178,182,183,185,187,190,194,201
%N A325161 Nonprime squarefree numbers not divisible by any two consecutive primes.
%C A325161 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).
%H A325161 Amiram Eldar, <a href="/A325161/b325161.txt">Table of n, a(n) for n = 1..10000</a>
%e A325161 The sequence of terms together with their prime indices begins:
%e A325161    1: {}
%e A325161   10: {1,3}
%e A325161   14: {1,4}
%e A325161   21: {2,4}
%e A325161   22: {1,5}
%e A325161   26: {1,6}
%e A325161   33: {2,5}
%e A325161   34: {1,7}
%e A325161   38: {1,8}
%e A325161   39: {2,6}
%e A325161   46: {1,9}
%e A325161   51: {2,7}
%e A325161   55: {3,5}
%e A325161   57: {2,8}
%e A325161   58: {1,10}
%e A325161   62: {1,11}
%e A325161   65: {3,6}
%e A325161   69: {2,9}
%e A325161   74: {1,12}
%e A325161   82: {1,13}
%t A325161 Select[Range[100],!PrimeQ[#]&&Min@@Differences[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]>1&]
%Y A325161 Cf. A001227, A003114, A005117, A025157, A034296, A056239, A073485, A073491, A089995, A112798, A116931, A319630, A325160, A325162.
%K A325161 nonn
%O A325161 1,2
%A A325161 _Gus Wiseman_, Apr 05 2019