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A322817 a(n) = A001222(A065642(n)) - A001222(n), where A065642(n) gives the next larger m that has same prime factors as n (ignoring multiplicity), and A001222 gives the number of prime factors, when counted with multiplicity. 2
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 0, 1, 1, -1, 1, 2, 1, 1, 1, 1, 1, -1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 2, 1, 2, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,50

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = A001222(A065642(n)) - A001222(n).

EXAMPLE

For n = 2 = 2^1, the next larger number with only 2's as its prime factors is 4 = 2^2, thus a(2) = 1.

For n = 12 = 2^2 * 3^1, the next larger number with the same prime factors is 18 = 2^1 * 3^2, with the same value of A001222, thus a(12) = 0.

For n = 40 = 2^3 * 5^1, the next larger number with the same prime factors is 50 = 2^1 * 5^2. While 40 has 3+1 = 4 prime factors in total, 50 has 1+2 = 3, thus a(40) = 3 - 4 = -1.

For n = 50, the next larger number with the same prime factors is 80 = 2^4 * 5^1, thus a(50) = (4+1)-(2+1) = 2.

PROG

(PARI)

A007947(n) = factorback(factorint(n)[, 1]);

A065642(n) = { my(r=A007947(n)); if(1==n, n, n = n+r; while(A007947(n) <> r, n = n+r); n); };

A322817(n) = (bigomega(A065642(n)) - bigomega(n));

CROSSREFS

Cf. A001222, A065642, A322818.

Sequence in context: A338639 A249351 A123706 * A194325 A300547 A025452

Adjacent sequences:  A322814 A322815 A322816 * A322818 A322819 A322820

KEYWORD

sign

AUTHOR

Antti Karttunen, Dec 27 2018

STATUS

approved

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Last modified September 24 13:43 EDT 2021. Contains 347643 sequences. (Running on oeis4.)