A109298 -id:A109298 - cp's OEIS frontend

A304194 Numbers k such that k = Product (p_j^e_j) = Product (pi(p_j)*p_j), where pi() = A000720.

1, 2, 12, 56, 180, 304, 336, 936, 1696, 1824, 2484, 5040, 5328, 6664, 8384, 8512, 9900, 10176, 13176, 14040, 25632, 26208, 27360, 33372, 33712, 37260, 39808, 39984, 47488, 50304, 51072, 52200, 65232, 69552, 79920, 126900, 128448, 142272, 149184, 152640, 162648, 167776, 184064, 193752, 197640

Offset: 1

Ilya Gutkovskiy, May 07 2018

nonn

Numbers k such that A007947(k)*A156061(k) = k or A156061(k) = A003557(k).

			9900 is a term because 9900 = 2^2 * 3^2 * 5^2 * 11 = prime(1)^2 * prime(2)^2 * prime(3)^2 * prime(5) = 1*prime(1) * 2*prime(2) * 3*prime(3) * 5*prime(5).

Eric Weisstein's World of Mathematics, Distinct Prime Factors
Index entries for sequences computed from indices in prime factorization

Cf. A000720, A003557, A005117, A007947, A008478, A033286, A046022, A048768, A078779, A109298, A156061.

a[n_] := Times @@ (PrimePi[#[[1]]] #[[1]] & /@ FactorInteger[n]); a[1] = 1; Select[Range[200000], a[#] == # &]

isok(n) = {my(f=factor(n)); prod(k=1, #f~, primepi(f[k,1])*f[k,1]) == n;} \\ Michel Marcus, May 08 2018

A306719 Lexicographically earliest sequence containing 2 and all positive integers n such that the prime indices of n - 1 already belong to the sequence.

Original entry on oeis.org

2, 4, 8, 10, 20, 22, 28, 30, 50, 58, 64, 72, 80, 82, 88, 108, 114, 134, 148, 172, 190, 204, 214, 230, 238, 244, 262, 272, 312, 322, 340, 344, 360, 362, 400, 410, 422, 442, 458, 498, 514, 552, 554, 568, 594, 610, 620, 640, 688, 712, 730, 750, 758, 784, 792, 814

Offset: 1

Gus Wiseman, Mar 11 2019

nonn

A self-describing sequence, similar to A304360.

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.

Prime indices of A324699.
Cf. A000002, A000720, A001222, A001462, A007097, A055396, A061395, A079000, A079254, A109298, A112798, A276625, A277098, A304360.
Cf. A324694, A324695, A324696, A324697, A324698, A324700, A324701, A324702, A324703, A324704, A324705.

aQ[n_]:=Switch[n,0,False,2,True,,And@@Cases[FactorInteger[n-1],{p,k_}:>aQ[PrimePi[p]]]];
Select[Range[0,100],aQ]

a(n) = A324699(n) + 1.

cp's OEIS Frontend

A304194 Numbers k such that k = Product (p_j^e_j) = Product (pi(p_j)*p_j), where pi() = A000720.

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