cp's OEIS Frontend

A339886 Numbers whose prime indices cover an interval of positive integers starting with 2.

%I A339886 #12 Apr 22 2021 01:43:01
%S A339886 1,3,9,15,27,45,75,81,105,135,225,243,315,375,405,525,675,729,735,945,
%T A339886 1125,1155,1215,1575,1875,2025,2187,2205,2625,2835,3375,3465,3645,
%U A339886 3675,4725,5145,5625,5775,6075,6561,6615,7875,8085,8505,9375,10125,10395,10935
%N A339886 Numbers whose prime indices cover an interval of positive integers starting with 2.
%C A339886 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.
%e A339886 The sequence of terms together with their prime indices begins:
%e A339886     3: {2}
%e A339886     9: {2,2}
%e A339886    15: {2,3}
%e A339886    27: {2,2,2}
%e A339886    45: {2,2,3}
%e A339886    75: {2,3,3}
%e A339886    81: {2,2,2,2}
%e A339886   105: {2,3,4}
%e A339886   135: {2,2,2,3}
%e A339886   225: {2,2,3,3}
%e A339886   243: {2,2,2,2,2}
%e A339886   315: {2,2,3,4}
%e A339886   375: {2,3,3,3}
%e A339886   405: {2,2,2,2,3}
%e A339886   525: {2,3,3,4}
%e A339886   675: {2,2,2,3,3}
%e A339886   729: {2,2,2,2,2,2}
%e A339886   735: {2,3,4,4}
%e A339886   945: {2,2,2,3,4}
%t A339886 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A339886 normQ[m_]:=Or[m=={},Union[m]==Range[Max[m]]];
%t A339886 Select[Range[100],normQ[primeMS[#]-1]&]
%Y A339886 The version starting at 1 is A055932.
%Y A339886 The partitions with these Heinz numbers are counted by A264396.
%Y A339886 Positions of 1's in A339662.
%Y A339886 A000009 counts partitions covering an initial interval.
%Y A339886 A000070 counts partitions with a selected part.
%Y A339886 A016945 lists numbers with smallest prime index 2.
%Y A339886 A034296 counts gap-free (or flat) partitions.
%Y A339886 A056239 adds up prime indices, row sums of A112798.
%Y A339886 A073491 lists numbers with gap-free prime indices.
%Y A339886 A107428 counts gap-free compositions (initial: A107429).
%Y A339886 A286469 and A286470 give greatest difference for Heinz numbers.
%Y A339886 A325240 lists numbers with smallest prime multiplicity 2.
%Y A339886 A342050/A342051 have prime indices with odd/even least gap.
%Y A339886 Cf. A001223, A001522, A006128, A007052, A124010, A257989, A257993, A264401, A317090, A317589, A339737.
%K A339886 nonn
%O A339886 1,2
%A A339886 _Gus Wiseman_, Apr 20 2021