cp's OEIS Frontend

A322553 Odd numbers whose product of prime indices is a prime power.

%I A322553 #7 Dec 16 2018 17:58:55
%S A322553 1,3,5,7,9,11,17,19,21,23,25,27,31,41,49,53,57,59,63,67,81,83,97,103,
%T A322553 109,115,121,125,127,131,133,147,157,159,171,179,189,191,211,227,241,
%U A322553 243,277,283,289,311,331,343,353,361,367,371,393,399,401,419,431,441
%N A322553 Odd numbers whose product of prime indices is a prime power.
%C A322553 Differs from A322400 in having 1 and lacking 377, the MM-number of {{1,2},{1,3}}.
%C A322553 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 A322553 The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}. The sequence of multiset partitions whose MM-numbers belong to this sequence begins:
%e A322553    1: {}
%e A322553    3: {{1}}
%e A322553    5: {{2}}
%e A322553    7: {{1,1}}
%e A322553    9: {{1},{1}}
%e A322553   11: {{3}}
%e A322553   17: {{4}}
%e A322553   19: {{1,1,1}}
%e A322553   21: {{1},{1,1}}
%e A322553   23: {{2,2}}
%e A322553   25: {{2},{2}}
%e A322553   27: {{1},{1},{1}}
%e A322553   31: {{5}}
%e A322553   41: {{6}}
%e A322553   49: {{1,1},{1,1}}
%e A322553   53: {{1,1,1,1}}
%e A322553   57: {{1},{1,1,1}}
%e A322553   59: {{7}}
%e A322553   63: {{1},{1},{1,1}}
%e A322553   67: {{8}}
%e A322553   81: {{1},{1},{1},{1}}
%e A322553   83: {{9}}
%e A322553   97: {{3,3}}
%t A322553 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A322553 Select[Range[1,100,2],#==1||PrimePowerQ[Times@@primeMS[#]]&]
%o A322553 (PARI) isok(n) = {if (n % 2, my(f = factor(n), pk = prod(k=1, #f~, primepi(f[k,1]))); (pk == 1) || isprimepower(pk););} \\ _Michel Marcus_, Dec 16 2018
%Y A322553 Cf. A003963, A056239, A112798, A290103, A302242, A320325, A320698.
%K A322553 nonn
%O A322553 1,2
%A A322553 _Gus Wiseman_, Dec 15 2018