login
A326810
The smallest prime that does not divide the prime product form (A276086) of the primorial base expansion of n.
8
2, 3, 2, 5, 2, 5, 2, 3, 2, 7, 2, 7, 2, 3, 2, 7, 2, 7, 2, 3, 2, 7, 2, 7, 2, 3, 2, 7, 2, 7, 2, 3, 2, 5, 2, 5, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11, 2, 11, 2, 3, 2, 5, 2, 5, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11, 2, 11, 2, 3, 2, 5, 2, 5, 2, 3, 2, 11, 2, 11, 2, 3, 2, 11
OFFSET
0,1
FORMULA
a(n) = A053669(A276086(n)).
a(n) = A000040(A328570(n)).
a(n) = A020639(A276087(n)) = A020639(A328613(n)).
a(n) = A276087(n) / A276086(A328476(n)).
For all odd n, a(n) > A276088(n).
For all n >= 0, a(A276086(n)) = A328579(n).
For all n >= 1, A328317(n) = a(A328316(n-1)).
MATHEMATICA
With[{b = MixedRadix[Reverse@ Prime@ Range@ 12]}, Table[Block[{p = 2}, While[Mod[#, p] == 0, p = NextPrime@ p]; p] &@ Apply[Times, Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #}] &@ IntegerDigits[n, b], {n, 0, 105}]] (* Michael De Vlieger, Oct 22 2019 *)
PROG
(PARI) A326810(n) = { my(i=1, p=2); while(n && (n%p), n = n\p; p = nextprime(1+p)); (p); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 19 2019
STATUS
approved