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Search: id:A141564
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| A141564 |
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Subtract 1 from all bases and exponents which are greater than 1 in the prime number decomposition of n. |
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+0
1
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| 0, 1, 2, 1, 4, 2, 6, 1, 2, 4, 10, 2, 12, 6, 8, 1, 16, 2, 18, 4, 12, 10, 22, 2, 4, 12, 4, 6, 28, 8, 30, 1, 20, 16, 24, 2, 36, 18, 24, 4, 40, 12, 42, 10, 8, 22, 46, 2, 6, 4, 32, 12, 52, 4, 40, 6, 36, 28, 58, 8, 60, 30, 12, 1, 48, 20, 66, 16, 44, 24, 70, 2, 72, 36, 8, 18, 60, 24, 78, 4, 8
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Start from the prime number decomposition of n, that is the list 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3... Subtract 1 from all visible bases and exponents (visible in the sense that exponents are not written down if they equal 1), to give 1-1, 2-1, 3-1, (2-1)^(2-1), 5-1, (2-1)*(3-1), 7-1, (2-1)^(3-1), (3-1)^(2-1), (2-1)*(5-1), 11-1, (2-1)^(2-1)*(3-1)..). Evaluate this modified product to yield a(n).
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MAPLE
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A := proc(n) local a, p, e, q, ifs ; if n = 1 then RETURN(0) ; fi; ifs := ifactors(n)[2] ; a := 1; for p in ifs do q := op(1, p)-1 ; if op(2, p) > 1 then e := op(2, p)-1 ; else e := 1 ; fi; a := a*q^e ; od: RETURN(a) ; end: for n from 1 to 120 do printf("%d, ", A(n)) ; od: # R. J. Mathar, Aug 21 2008
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CROSSREFS
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Cf. A000040, A002808.
Sequence in context: A098371 A070777 A023900 this_sequence A046791 A125131 A003958
Adjacent sequences: A141561 A141562 A141563 this_sequence A141565 A141566 A141567
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KEYWORD
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nonn
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Aug 14 2008
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 21 2008
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