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A352823
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Number of nonfixed points y(i) != i, where y is the weakly increasing sequence of prime indices of n.
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10
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0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 2, 2, 1, 0, 1, 4, 2, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 3, 1, 1, 2, 5, 2, 1, 1, 2, 2, 2, 1, 4, 1, 1, 2, 2, 2, 1, 1, 4, 3, 1, 1, 2, 2, 1, 2, 3, 1, 2, 2, 2, 2, 1, 2, 5, 1, 2, 2, 2, 1, 1, 1, 3, 3
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OFFSET
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1,8
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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FORMULA
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EXAMPLE
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The prime indices of 6500 are {1,1,3,3,3,6}, with nonfixed points at positions {2,4,5}, so a(6500) = 3.
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MATHEMATICA
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pnq[y_]:=Length[Select[Range[Length[y]], #!=y[[#]]&]];
Table[pnq[If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]], {n, 100}]
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PROG
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(PARI) A352823(n) = { my(f=factor(n), i=0, c=0); for(k=1, #f~, while(f[k, 2], f[k, 2]--; i++; c += (i!=primepi(f[k, 1])))); (c); }; \\ Antti Karttunen, Apr 11 2022
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CROSSREFS
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* = unproved
Positions of first appearances are A077552.
The complement triangle version is A238352.
A122111 represents partition conjugation using Heinz numbers.
A238394 counts reversed partitions without a fixed point, ranked by A352830.
A238395 counts reversed partitions with a fixed point, ranked by A352872.
Cf. A065770, A093641, A114088, A252464, A257990, A325163, A325164, A325165, A325169, A342192, A352486-A352491, A352828, A352829.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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