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A328572
Primorial base expansion of n converted into its prime product form, but with 1 subtracted from all nonzero digits: a(n) = A003557(A276086(n)).
37
1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 15, 15, 25, 25, 25, 25, 75, 75, 125, 125, 125, 125, 375, 375, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 15, 15, 25, 25, 25, 25, 75, 75, 125, 125, 125, 125, 375, 375, 7, 7, 7, 7, 21, 21, 7, 7, 7, 7, 21, 21, 35, 35, 35, 35, 105, 105, 175, 175, 175, 175, 525, 525, 875, 875, 875, 875
OFFSET
0,5
FORMULA
a(n) = A003557(A276086(n)).
a(n) = A276086(n) / A328571(n).
a(n) = A328475(n) / A328573(n).
For all n >= 1, 1+A051903(a(n)) = A328114(n).
a(n) = A085731(A276086(n)) = gcd(A276086(n), A327860(n)). - Antti Karttunen, Feb 28 2021
MATHEMATICA
Block[{b = MixedRadix[Reverse@ Prime@ Range@ 12]}, Array[#1/(Times @@ #2[[All, 1]]) & @@ {#1, FactorInteger[#]} &[Times @@ Power @@@ #] &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[#, b] &, 87, 0]] (* Michael De Vlieger, Mar 12 2021 *)
PROG
(PARI) A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Oct 20 2019
STATUS
approved