A347249 -id:A347249 - cp's OEIS frontend

A347375 The position of the first occurrence of n in A347249.

1, 15, 25, 75, 275, 725, 2175, 3725, 9025, 27075, 79025, 215905, 390625, 1079525, 2256125, 5397625, 11328125, 33984375, 58203125, 174609375

Offset: 0

Antti Karttunen, Aug 31 2021

These appear to also be the positions of records in A347249.

Question: Are all terms after the initial one multiples of five?

Cf. A331410, A336361, A347249, A347374.

For all n >= 0, A347249(a(n)) = n.

A336361 Number of iterations of A000593 (sum of divisors of odd part of n) needed to reach a power of 2, or -1 if never reached.

Original entry on oeis.org

0, 0, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 2, 0, 4, 3, 3, 2, 1, 2, 2, 1, 2, 2, 3, 1, 3, 2, 1, 0, 2, 4, 2, 3, 4, 3, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 4, 2, 4, 2, 4, 3, 4, 1, 3, 3, 3, 2, 2, 1, 3, 0, 2, 2, 5, 4, 2, 2, 4, 3, 5, 4, 2, 3, 2, 2, 3, 2, 5, 2, 2, 1, 4, 3, 3, 2, 4, 3, 2, 2, 1, 2, 3, 1, 5, 4, 3, 2, 5, 4, 3, 2, 2

Offset: 1

Antti Karttunen, Jul 30 2020

nonn

Also, for n > 1, one less than the number of iterations of A000593 to reach 1.

If there exists any hypothetical odd perfect numbers w, then the iteration will get stuck into a fixed point after encountering them, and we will have a(w) = a(2^k * w) = -1 by the escape clause.

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

Cf. A000265, A000593, A161942, A209229, A336362, A336363, A347249, A347250.
Cf. A054784 (positions of 0's and 1's in this sequence).
Cf. also A347240, A347241, A347242, A347243, A347244, A347245.

A336361(n) = if(!bitand(n,n-1),0,1+A336361(sigma(n>>valuation(n,2))));

If A209229(n) = 1 [when n is a power of 2], a(n) = 0, otherwise a(n) = 1+a(A000593(n)).

a(n) = a(2n) = a(A000265(n)).

A347374 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A000593(i) = A000593(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 17, 5, 18, 10, 19, 3, 20, 11, 21, 6, 22, 12, 23, 2, 24, 13, 25, 7, 26, 14, 25, 4, 27, 15, 28, 8, 29, 16, 30, 1, 31, 17, 32, 9, 33, 17, 34, 5, 35, 18, 36, 10, 33, 19, 37, 3, 38, 20, 39, 11, 40, 21, 41, 6, 42, 22, 43, 12

Offset: 1

Antti Karttunen, Aug 29 2021

nonn

Restricted growth sequence transform of the ordered pair [A000593(n), A331410(n)].

For all i, j: A003602(i) = A003602(j) => a(i) = a(j) => A347249(i) = A347249(j).

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

Cf. A000593, A003602, A331410, A347249.

Cf. also A335880, A336390, A336391, A336394 for similar constructions.

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; };
A000593(n) = sigma(n>>valuation(n, 2));
A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
Aux347374(n) = [A331410(n), A000593(n)];
v347374 = rgs_transform(vector(up_to, n, Aux347374(n)));
A347374(n) = v347374[n];

A347250 Numbers k for which A331410(k) < A336361(k).

Original entry on oeis.org

9, 17, 18, 34, 36, 49, 67, 68, 71, 72, 81, 97, 98, 134, 136, 142, 144, 147, 162, 193, 194, 196, 268, 271, 272, 283, 284, 288, 291, 293, 294, 324, 386, 388, 392, 536, 541, 542, 544, 566, 568, 576, 579, 582, 586, 587, 588, 647, 648, 679, 772, 776, 784, 961, 1072, 1082, 1084, 1087, 1088, 1132, 1136, 1151, 1152, 1158, 1163

Offset: 1

Antti Karttunen, Aug 28 2021

nonn

If k is a term, then also 2*k is present in this sequence.

Cf. A331410, A336361.

Positions of negative terms in A347249.

A331410(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+A331410(f[k,1]+1)))); };
A336361(n) = if(!bitand(n,n-1),0,1+A336361(sigma(n>>valuation(n,2))));
A347249(n) = (A331410(n)-A336361(n));
isA347250(n) = (A347249(n)<0);

cp's OEIS Frontend

A347375 The position of the first occurrence of n in A347249.

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A336361 Number of iterations of A000593 (sum of divisors of odd part of n) needed to reach a power of 2, or -1 if never reached.

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A347374 Lexicographically earliest infinite sequence such that a(i) = a(j) => A331410(i) = A331410(j) and A000593(i) = A000593(j), for all i, j >= 1.

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A347250 Numbers k for which A331410(k) < A336361(k).

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