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A319994 Let g = A006530(n), the largest prime factor of n. This filter sequence combines (g mod 4), n/g (A052126), and a single bit A319988(n) telling whether the largest prime factor is unitary. 5
1, 2, 3, 4, 5, 6, 3, 7, 8, 9, 3, 10, 5, 6, 11, 12, 5, 13, 3, 14, 15, 6, 3, 16, 17, 9, 18, 10, 5, 19, 3, 20, 15, 9, 21, 22, 5, 6, 11, 23, 5, 24, 3, 10, 25, 6, 3, 26, 27, 28, 11, 14, 5, 29, 21, 16, 15, 9, 3, 30, 5, 6, 31, 32, 33, 24, 3, 14, 15, 34, 3, 35, 5, 9, 36, 10, 37, 19, 3, 38, 39, 9, 3, 40, 33, 6, 11, 16, 5, 41, 42, 10, 15, 6, 21, 43, 5, 44, 31, 45, 5, 19, 3, 23, 46 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Restricted growth sequence transform of triple [A010873(A006530(n)), A052126(n), A319988(n)], with a separate value allotted for a(1).

Here among the first 100000 terms, only 2331 have a unique value, compared to 69714 in A320004.

For all i, j:

  a(i) = a(j) => A024362(i) = A024362(j),

  a(i) = a(j) => A067029(i) = A067029(j),

  a(i) = a(j) => A071178(i) = A071178(j),

  a(i) = a(j) => A077462(i) = A077462(j) => A101296(i) = A101296(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

PROG

(PARI)

up_to = 100000;

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

A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);

A052126(n) = (n/A006530(n));

A319988(n) = ((n>1)&&(factor(n)[omega(n), 2]>1));

A319994aux(n) = if(1==n, 0, [A006530(n)%4, A052126(n), A319988(n)]);

v319994 = rgs_transform(vector(up_to, n, A319994aux(n)));

A319994(n) = v319994[n];

CROSSREFS

Cf. A006530, A052126, A319988, A320004.

Cf. also A319996 (modulo 6 analog).

Sequence in context: A274630 A278058 A320115 * A319714 A320004 A319704

Adjacent sequences:  A319991 A319992 A319993 * A319995 A319996 A319997

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 05 2018

STATUS

approved

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Last modified November 14 01:24 EST 2019. Contains 329108 sequences. (Running on oeis4.)