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A331119
Indices of A025487(n) in A055932.
1
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
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
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Feb 01 2020
STATUS
approved