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A120636
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a(1) = 1. Replace each prime power in the prime factorization of n with the next lower prime power.
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3
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1, 1, 2, 3, 4, 2, 5, 7, 8, 4, 9, 6, 11, 5, 8, 13, 16, 8, 17, 12, 10, 9, 19, 14, 23, 11, 25, 15, 27, 8, 29, 31, 18, 16, 20, 24, 32, 17, 22, 28, 37, 10, 41, 27, 32, 19, 43, 26, 47, 23, 32, 33, 49, 25, 36, 35, 34, 27, 53, 24, 59, 29, 40, 61, 44, 18, 64, 48, 38, 20, 67, 56, 71, 32, 46, 51
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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EXAMPLE
| 50 = 2^1 *5^2. 1 is the prime power closest to 2 and smaller than 2. 23 is the prime power closest to 5^2 and smaller than 5^2. So a(50) = 1*23 = 23.
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PROG
| (PARI) { a(n) = local(f, r, k, d); f=factorint(n); r=1; for(i=1, matsize(f)[1], k=f[i, 1]^f[i, 2]-1; while(k>1 && !isprime(k) && (!ispower(k, , &d)||!isprime(d)), k--); r*=k); r } - Max Alekseyev (maxale(AT)gmail.com), Mar 26 2007
(Sage) def A120636(n): return prod((previous_prime_power(p**m) for p, m in factor(n)) if n > 1 else 1 # [D. S. McNeil, Feb 09 2011]
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CROSSREFS
| Cf. A120635.
Sequence in context: A161759 A157000 A026346 * A117744 A091732 A109746
Adjacent sequences: A120633 A120634 A120635 * A120637 A120638 A120639
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KEYWORD
| nonn,mult
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AUTHOR
| Leroy Quet Jun 22 2006
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Mar 26 2007
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