A332035 - OEIS

%I #7 Feb 06 2020 18:39:46

%S 1,2,3,4,6,9,12,13,15,21,26,30,36,49,53,63,72,86,114,149,175,212,221,

%T 285,367,424,505,541,643,687,703,886,1015,1198,1272,1496,1586,1704,

%U 2116,2491,2912,3076,3587,3791,4052,4971,5999,6087,6845,6955,7330,8481,8933

%N Indices of A004394(n) in A055932.

%C 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.

%H Michael De Vlieger, <a href="/A332035/b332035.txt">Table of n, a(n) for n = 1..166</a>

%t 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]]]

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

%K nonn

%O 1,2

%A _Michael De Vlieger_, Feb 05 2020