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

1,2

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

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]]]

Crossrefs

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

Sequence in context: A377151 A288734 A332034 * A318759 A018471 A240307

Adjacent sequences: A332032 A332033 A332034 * A332036 A332037 A332038

Keyword

nonn

Author

Michael De Vlieger, Feb 05 2020

Status

approved