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A328613
Starting with m = 1, p = 2 and x = n, iterate m -> m * p^valuation(x,p), x -> floor(x/p), p -> {the next prime after p}, until x is zero. Then a(n) = product of the values of m and p that were reached at the end of the iteration.
7
2, 3, 10, 5, 20, 5, 42, 21, 56, 7, 14, 7, 84, 21, 14, 7, 112, 7, 126, 63, 28, 7, 14, 7, 168, 21, 14, 7, 28, 7, 330, 165, 1760, 55, 110, 55, 396, 99, 22, 11, 88, 11, 66, 33, 44, 11, 22, 11, 528, 33, 22, 11, 44, 11, 594, 297, 88, 11, 22, 11, 660, 165, 110, 55, 3520, 55, 66, 33, 44, 11, 22, 11, 792, 99, 22, 11, 44, 11, 66, 33, 176, 11
OFFSET
0,1
FORMULA
a(n) = A000040(1+A235224(n)) * A328612(n).
For all n >= 0, A055396(a(n)) = A328570(n) and A020639(a(n)) = A326810(n).
For all n >= 1, A007814(a(n)) = A007814(n).
For all n >= 1, a(A143293(n-1)) = A000040(1+n).
PROG
(PARI) A328613(n) = { my(m=1, p=2); while(n, m *= p^valuation(n, p); n = n\p; p = nextprime(1+p)); (m*p); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 22 2019
STATUS
approved