A253550 - OEIS

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A253550

Shift one instance of the largest prime one step towards larger primes: a(1) = 1, for n>1: a(n) = (n / prime(g)) * prime(g+1), where g = A061395(n), index of the greatest prime dividing n.

1, 3, 5, 6, 7, 10, 11, 12, 15, 14, 13, 20, 17, 22, 21, 24, 19, 30, 23, 28, 33, 26, 29, 40, 35, 34, 45, 44, 31, 42, 37, 48, 39, 38, 55, 60, 41, 46, 51, 56, 43, 66, 47, 52, 63, 58, 53, 80, 77, 70, 57, 68, 59, 90, 65, 88, 69, 62, 61, 84, 67, 74, 99, 96, 85, 78, 71, 76, 87, 110, 73, 120, 79, 82, 105, 92, 91, 102, 83, 112, 135, 86, 89

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(1) = 1; for n>1: a(n) = A065091(A061395(n)) * A052126(n).

Other identities. For all n >= 1:

A252462(a(n)) = n. [A252462 works as an inverse function for this injection.]

a(n) <= A253560(n).

PROG

(Scheme) (define (A253550 n) (if (= 1 n) n (* (A065091 (A061395 n)) (A052126 n))))