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 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).
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
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Aug 14 2008
EXTENSIONS
Corrected and extended by R. J. Mathar, Aug 21 2008
STATUS
approved