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A179983
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Positive integers n such that, if k appears in n's prime signature, k-1 appears at least as often as k (for any integer k > 1).
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5
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1, 2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 89, 90
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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The prime signature of 20 = 2^2*5 is (2,1). Since the largest number appearing in 20's prime signature is 2, and 1 appears as many times as 2, 20 is a member of this sequence.
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MAPLE
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isA179983 := proc(n)
local es, me, k ;
# list of exponents in prime signature
es := [seq(op(2, pe), pe =ifactors(n)[2])] ;
# maximum exponent
me := max(op(es)) ;
for k from me to 2 by -1 do
if numboccur(es, k-1) < numboccur(es, k) then
return false;
end if;
end do:
true ;
end proc:
for n from 1 to 100 do
if isA179983(n) then
printf("%d, ", n) ;
end if;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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