A347376 - OEIS

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A347376

Möbius transform of A250469.

1, 2, 4, 6, 6, 8, 10, 12, 20, 18, 12, 12, 16, 26, 24, 24, 18, 16, 22, 24, 40, 48, 28, 24, 42, 56, 40, 36, 30, 24, 36, 48, 68, 78, 60, 36, 40, 86, 74, 48, 42, 32, 46, 60, 60, 104, 52, 48, 110, 78, 102, 72, 58, 68, 72, 72, 118, 138, 60, 48, 66, 144, 80, 96, 96, 52, 70, 96, 142, 84, 72, 72, 78, 176, 108, 108, 120, 70

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OFFSET

1,2

COMMENTS

Question: Are all terms positive?

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences generated by sieves

FORMULA

a(n) = Sum_{d|n} A008683(n/d) * A250469(d).

a(n) = A003972(n) - A347377(n).

PROG

(PARI)

up_to = 10000;

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; };

A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639

v078898 = ordinal_transform(vector(up_to, n, A020639(n)));

A078898(n) = v078898[n];

A250469(n) = if(1==n, n, my(spn = nextprime(1+A020639(n)), c = A078898(n), k = 0); while(c, k++; if((1==k)||(A020639(k)>=spn), c -= 1)); (k*spn));

A347376(n) = sumdiv(n, d, moebius(n/d)*A250469(d));

CROSSREFS

Cf. A003972, A008683, A020639, A078898, A250469, A347377.

Cf. also A346479.

Sequence in context: A082990 A099188 A085271 * A260812 A003972 A023853

Adjacent sequences: A347373 A347374 A347375 * A347377 A347378 A347379

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 01 2021

STATUS

approved