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A296086 Filter sequence combining A003557(n), A048250(n) and A173557(n). 4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The first point where this differs from A000027 is at 15265, where a(15265) = 15169. A296087 gives the positions of each subsequent (not initial) occurrence for the duplicated terms.

For all i, j:

  a(i) = a(j) => A291750(i) = A291750(j).

  a(i) = a(j) => A295887(i) = A295887(j).

  a(i) = a(j) => A296085(i) = A296085(j).

LINKS

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

PROG

(PARI)

up_to = 65537;

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; };

write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0, f[i, 2]-1)); factorback(f); };

A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));

A173557(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ This function from Michel Marcus, Oct 31 2017

Anotsubmitted1(n) = (1/2)*(2 + ((A003557(n)+A173557(n))^2) - A003557(n) - 3*A173557(n));

Anotsubmitted2(n) = (1/2)*(2 + ((A048250(n)+Anotsubmitted1(n))^2) - A048250(n) - 3*Anotsubmitted1(n));

write_to_bfile(1, rgs_transform(vector(up_to, n, Anotsubmitted2(n))), "b296086.txt");

CROSSREFS

Cf. A003557, A048250, A173557, A291750, A295887, A296085, A296087.

Sequence in context: A001477 A087156 A254109 * A292579 A262530 A291179

Adjacent sequences:  A296083 A296084 A296085 * A296087 A296088 A296089

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 08 2017

STATUS

approved

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Last modified February 19 11:02 EST 2018. Contains 299330 sequences. (Running on oeis4.)