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A331186 Exponent of the highest power of prime(A067004(n)) which divides n, where A067004 is the ordinal transform of number of divisors of n (A000005). 3
0, 1, 1, 2, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 0, 4, 1, 2, 1, 1, 0, 0, 1, 3, 2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 4, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 6, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = A286561(n, A000040(A067004(n))), where A286561(n,k) gives the k-valuation of n.

PROG

(PARI)

up_to = 65537;

ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };

v067004 = ordinal_transform(vector(up_to, n, numdiv(n)));

A067004(n) = v067004[n];

A331186(n) = valuation(n, prime(A067004(n)));

CROSSREFS

Cf. A000005, A067004, A286561.

Cf. also A331185, A331187.

Sequence in context: A117162 A277045 A146061 * A135936 A109707 A214578

Adjacent sequences:  A331183 A331184 A331185 * A331187 A331188 A331189

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 12 2020

STATUS

approved

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Last modified September 20 04:38 EDT 2021. Contains 347577 sequences. (Running on oeis4.)