A331119 Indices of A025487(n) in A055932.

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, 33, 36, 37, 38, 39, 41, 43, 45, 49, 51, 53, 54, 55, 56, 58, 60, 61, 63, 64, 66, 70, 72, 73, 74, 76, 78, 80, 82, 83, 86, 87, 89, 93, 96, 97, 98, 101, 104, 106, 110, 111

Offset

1,2

Comments

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.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 since the empty product is the first term in both sequences.
a(2) = 2 since 2 is the smallest prime and appears in both sequences after 1.
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).
a(8) = 9 since A025487(8) = 24 = A055932(9).

Mathematica

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] ]

Crossrefs

Cf. A002110, A025487, A055932.

Sequence in context: A316228 A353935 A348782 * A366169 A283970 A376268

Adjacent sequences: A331116 A331117 A331118 * A331120 A331121 A331122

Keyword

nonn

Author

Michael De Vlieger, Feb 01 2020

Status

approved