A355701 a(n) = Product of prime(k+1) where k runs through the exponents of the positions 2^k of the 1-bits in A354169(n).

1, 2, 3, 5, 7, 6, 11, 13, 17, 35, 19, 23, 29, 22, 31, 39, 37, 41, 43, 85, 47, 133, 53, 59, 61, 667, 67, 71, 73, 62, 79, 33, 83, 481, 89, 97, 101, 1763, 103, 107, 109, 235, 113, 119, 127, 1007, 131, 137, 139, 3599, 149, 151, 157, 1541, 163, 2059, 167, 173, 179

Offset: 0

Author

Michael De Vlieger, Jul 14 2022

Keywords

• nonn

Comments

Compactification of A354169. Offset matches A354169.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Michael De Vlieger, Annotated plot of prime factors p | a(n) at (n, pi(p)) for n = 0..50.

Crossrefs

Cf. A005117, A090252, A354169.

Programs

Mathematica

nn = 58; r = c[] = 0; m = 1; Array[Set[{a[#], c[#]}, {#, #}] &, 2, 0]; Do[k = SelectFirst[Union@ Map[Total, Rest@ Subsets[2^Reverse[Length[#] - Position[#, 1][[All, 1]]] &@ IntegerDigits[2^(r + 2) - m - 1, 2]]], c[#] == 0 &]; Set[{a[n], c[k]}, {k, n}]; m += a[n]; If[And[IntegerQ[#], # > 0], m -= a[#]] &[n/2]; If[And[EvenQ[k], PrimePowerQ[k], k > 2^r], r++], {n, 2, nn}]; Table[Times @@ Map[Prime, 1 + Length[#] - Position[#, 1][[All, 1]]] &@ IntegerDigits[a[n], 2], {n, 0, nn}] (* _Michael De Vlieger, Jul 14 2022 *)