cp's OEIS Frontend

A325091 Heinz numbers of integer partitions of powers of 2.

%I A325091 #12 Mar 28 2019 09:23:15
%S A325091 1,2,3,4,7,9,10,12,16,19,34,39,49,52,53,55,63,66,70,75,81,84,88,90,94,
%T A325091 100,108,112,120,129,131,144,160,172,192,205,246,254,256,259,311,328,
%U A325091 333,339,341,361,370,377,391,434,444,452,465,545,558,592,598,609,614
%N A325091 Heinz numbers of integer partitions of powers of 2.
%C A325091 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k), so these are numbers whose sum of prime indices is a power of 2. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A325091 1 is in the sequence because it has prime indices {} with sum 0 = 2^(-infinity).
%e A325091 The sequence of terms together with their prime indices begins:
%e A325091    1: {}
%e A325091    2: {1}
%e A325091    3: {2}
%e A325091    4: {1,1}
%e A325091    7: {4}
%e A325091    9: {2,2}
%e A325091   10: {1,3}
%e A325091   12: {1,1,2}
%e A325091   16: {1,1,1,1}
%e A325091   19: {8}
%e A325091   34: {1,7}
%e A325091   39: {2,6}
%e A325091   49: {4,4}
%e A325091   52: {1,1,6}
%e A325091   53: {16}
%e A325091   55: {3,5}
%e A325091   63: {2,2,4}
%e A325091   66: {1,2,5}
%e A325091   70: {1,3,4}
%e A325091   75: {2,3,3}
%e A325091   81: {2,2,2,2}
%p A325091 q:= n-> (t-> t=2^ilog2(t))(add(numtheory[pi](i[1])*i[2], i=ifactors(n)[2])):
%p A325091 select(q, [$1..1000])[];  # _Alois P. Heinz_, Mar 28 2019
%t A325091 Select[Range[100],#==1||IntegerQ[Log[2,Total[Cases[FactorInteger[#],{p_,k_}:>k*PrimePi[p]]]]]&]
%Y A325091 Cf. A000720, A001222, A018819, A033844, A056239, A102378, A112798, A131577, A318400, A325092, A325093.
%K A325091 nonn
%O A325091 1,2
%A A325091 _Gus Wiseman_, Mar 27 2019