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proposed

Positions of records (first appearances) areappear to be A006005A116974.

allocatedGCD of the prime indices of forn, all Gusplus Wiseman1.

0, 2, 3, 2, 4, 1, 5, 2, 3, 2, 6, 1, 7, 1, 1, 2, 8, 1, 9, 2, 1, 2, 10, 1, 4, 1, 3, 1, 11, 1, 12, 2, 3, 2, 1, 1, 13, 1, 1, 2, 14, 1, 15, 2, 1, 2, 16, 1, 5, 2, 1, 1, 17, 1, 2, 1, 3, 1, 18, 1, 19, 2, 1, 2, 1, 1, 20, 2, 1, 1, 21, 1, 22, 1, 1, 1, 1, 1, 23, 2, 3, 2

1,2

Zeros are ignored when computing GCD, and the empty set has GCD 0.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

a(n) = A289508(A003961(n)).

85 has prime indices {3,7}, so a(85) = GCD(4,8) = 4.

Table[GCD@@(PrimePi/@First/@If[n==1, {}, FactorInteger[n]]+1), {n, 100}]

Positions of 0's and 1's are A318981.

Positions of records (first appearances) are A006005.

The GCD of the prime indices of n, all minus 1, is A328167(n).

The LCM of the prime indices of n, all plus 1, is A328219(n).

Partitions whose parts plus 1 are relatively prime are A318980.

Cf. A000837, A056239, A112798, A258409, A289508, A289509, A290103, A328168.

allocated

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Gus Wiseman, Oct 09 2019

approved

editing

allocated for Gus Wiseman

allocated

approved