cp's OEIS Frontend

A371127 Powers of 2 times powers > 1 of a prime-indexed prime number.

%I A371127 #6 Mar 19 2024 08:38:08
%S A371127 3,5,6,9,10,11,12,17,18,20,22,24,25,27,31,34,36,40,41,44,48,50,54,59,
%T A371127 62,67,68,72,80,81,82,83,88,96,100,108,109,118,121,124,125,127,134,
%U A371127 136,144,157,160,162,164,166,176,179,191,192,200,211,216,218,236,241
%N A371127 Powers of 2 times powers > 1 of a prime-indexed prime number.
%C A371127 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 A371127 The terms together with their prime indices begin:
%e A371127       3: {2}
%e A371127       5: {3}
%e A371127       6: {1,2}
%e A371127       9: {2,2}
%e A371127      10: {1,3}
%e A371127      11: {5}
%e A371127      12: {1,1,2}
%e A371127      17: {7}
%e A371127      18: {1,2,2}
%e A371127      20: {1,1,3}
%e A371127      22: {1,5}
%e A371127      24: {1,1,1,2}
%e A371127      25: {3,3}
%e A371127      27: {2,2,2}
%e A371127      31: {11}
%e A371127      34: {1,7}
%e A371127      36: {1,1,2,2}
%t A371127 Select[Range[100],Length[Union @@ Divisors/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]]==2&]
%Y A371127 Subset of A302540.
%Y A371127 Subset of A336101 = powers of 2 times powers of primes.
%Y A371127 Positions of 2's in A370820.
%Y A371127 Counting prime factors instead of divisors gives A371287.
%Y A371127 A000005 counts divisors.
%Y A371127 A000961 lists powers of primes, A302596 of prime index.
%Y A371127 A001221 counts distinct prime factors.
%Y A371127 A003963 gives product of prime indices.
%Y A371127 A027746 lists prime factors, indices A112798, length A001222.
%Y A371127 A076610 lists products of primes of prime index.
%Y A371127 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A371127 A355741 counts choices of a prime factor of each prime index.
%Y A371127 Cf. A000079, A005179, A007416, A303975, A319899, A355739, A370348, A370802, A371165-A371170, A371178.
%K A371127 nonn
%O A371127 1,1
%A A371127 _Gus Wiseman_, Mar 18 2024