

A141564


Subtract 1 from all bases and exponents which are greater than 1 in the prime number decomposition of n.


1



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
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OFFSET

1,3


COMMENTS

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 11, 21, 31, (21)^(21), 51, (21)*(31), 71, (21)^(31), (31)^(21), (21)*(51), 111, (21)^(21)*(31)..). Evaluate this modified product to yield a(n).


LINKS

Table of n, a(n) for n=1..81.


MAPLE

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


CROSSREFS

Cf. A000040, A002808.
Sequence in context: A173614 A173557 A023900 * A239641 A249151 A046791
Adjacent sequences: A141561 A141562 A141563 * A141565 A141566 A141567


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Aug 14 2008


EXTENSIONS

Corrected and extended by R. J. Mathar, Aug 21 2008


STATUS

approved



