A324544 - OEIS

A324544

a(n) = A009194(A250246(n)) = gcd(A250246(n), A324545(n)).

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 12, 1, 2, 1, 28, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 3, 10, 1, 6, 1, 4, 1, 2, 1, 4, 1, 1, 1, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 18, 1, 2, 15, 2, 1, 3, 1, 2, 3, 4, 1, 6, 1, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 3, 1, 4, 1, 2, 1, 12, 1, 1, 1, 1, 1, 6, 1, 2, 1

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OFFSET

1,6

COMMENTS

Fixed points are: 1, 6, 28, 120, 496, 8128, etc,

Positions where a(n) == A250246(n) are: 1, 6, 28, 120, 496, 864, 8128, 11424, 15240, ..., which is sequence A250245(A007691(n)) sorted into ascending order.

LINKS

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

FORMULA

a(n) = A009194(A250246(n)) = gcd(A250246(n), A324545(n)).

a(n) = A324394(A252754(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; };

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

A055396(n) = if(1==n, 0, primepi(A020639(n)));

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

A078898(n) = v078898[n];

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961

A250246(n) = if(1==n, n, my(k = 2*A250246(A078898(n)), r = A055396(n)); if(1==r, k, while(r>1, k = A003961(k); r--); (k)));

A009194(n) = gcd(n, sigma(n));

A324544(n) = A009194(A250246(n));

CROSSREFS

Cf. A007691, A009194, A250246, A252754, A324394, A324545, A324546.

Differs from A009194 for the first time at n=39. Here a(39) = 3.

Sequence in context: A325640 A325632 A009194 * A323160 A323166 A007732

Adjacent sequences: A324541 A324542 A324543 * A324545 A324546 A324547

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 06 2019

STATUS

approved