A332035 Indices of A004394(n) in A055932.

1, 2, 3, 4, 6, 9, 12, 13, 15, 21, 26, 30, 36, 49, 53, 63, 72, 86, 114, 149, 175, 212, 221, 285, 367, 424, 505, 541, 643, 687, 703, 886, 1015, 1198, 1272, 1496, 1586, 1704, 2116, 2491, 2912, 3076, 3587, 3791, 4052, 4971, 5999, 6087, 6845, 6955, 7330, 8481, 8933

Offset: 1

Author

Michael De Vlieger, Feb 05 2020

Keywords

• nonn

Comments

A055932 lists numbers m whose prime divisors p are consecutive primes starting with 2, while A004394 is a subset of A025487, the latter lists numbers m that are products of primorials. With both, we find a range of indices of primes 1, 2, ..., k that divide m. While A055932 admits any multiplicity for primes regardless of their index, the latter only admits decreasing multiplicities as prime index k increases. A004394 is a subset of A025487, which is in turn a subset of A055932.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..166

Crossrefs

Cf. A004394, A025487, A055932, A293635 (Indices of A004394(n) in A025487), A332034.

Programs

Mathematica

Block[{s = TakeWhile[Import["https://oeis.org/A055932/b055932.txt", "Data"], Length@ # > 0 &][[All, -1]], t = Join @@ {Map[ToExpression@ Last@ StringSplit@ # &, #1][[All, -1]], Map[Times @@ Flatten@ {Complement[#1, Union[#2, #3]], Product[Prime@ i, {i, PrimePi@ #}] & /@ #2, Factorial /@ #3} & @@ ToExpression@ {StringSplit[#, _?(! DigitQ@ # &)], StringCases[#, (x : DigitCharacter ..) ~~ "#" :> x], StringCases[#, (x : DigitCharacter ..) ~~ "!" :> x]} &@ Last@ StringSplit[First[#]] &, TakeWhile[#2, Length@ # > 0 &]]} & @@ TakeDrop[Drop[#, 3] &@ Import["https://oeis.org/A004394/b004394.txt", "Data"], 2000] }, Reap[Do[Which[Length@ t == 0, Break[], First[t] == s[[i]] , t = Rest@ t; Sow[i]], {i, Length@ s}]][[-1, -1]]]