A331119 - OEIS

%I #7 Feb 01 2020 22:39:39

%S 1,2,3,4,5,6,7,9,10,11,12,13,15,16,17,19,21,22,23,26,27,28,29,30,31,

%T 33,36,37,38,39,41,43,45,49,51,53,54,55,56,58,60,61,63,64,66,70,72,73,

%U 74,76,78,80,82,83,86,87,89,93,96,97,98,101,104,106,110,111

%N Indices of A025487(n) in A055932.

%C A055932 lists numbers m whose prime divisors p are consecutive primes starting with 2, while A025487 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. Therefore, A025487 is a subset of A055932.

%H Michael De Vlieger, <a href="/A331119/b331119.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 1 since the empty product is the first term in both sequences.

%e a(2) = 2 since 2 is the smallest prime and appears in both sequences after 1.

%e 8 is not in the sequence, since A055932(8) = 18 = 2 * 3^2 and is not the product of primorials (or, rather, we can identify a smaller number - 12 - for the prime signature p^2 * q).

%e a(8) = 9 since A025487(8) = 24 = A055932(9).

%t With[{s = TakeWhile[Import["https://oeis.org/A025487/b025487.txt", "Data"], Length@ # > 0 &][[All, -1]], t = TakeWhile[Import["https://oeis.org/A055932/b055932.txt", "Data"], Length@ # > 0 &][[All, -1]]}, TakeWhile[Map[FirstPosition[t, #][[1]] &, s[[1 ;; 1000]]], IntegerQ] ]

%Y Cf. A002110, A025487, A055932.

%K nonn

%O 1,2

%A _Michael De Vlieger_, Feb 01 2020