A376690 First differences of A055932.

1, 2, 2, 2, 4, 4, 2, 6, 6, 2, 4, 12, 6, 6, 4, 8, 18, 6, 12, 12, 8, 16, 6, 12, 18, 12, 18, 6, 24, 16, 14, 18, 12, 24, 36, 24, 36, 12, 18, 30, 6, 26, 28, 36, 24, 30, 18, 72, 30, 18, 42, 30, 24, 36, 60, 12, 52, 26, 30, 72, 48, 60, 36, 54, 90, 18, 12, 30, 36, 84, 60

Offset

1,2

Comments

First difference of numbers k with a primorial kernel, i.e., rad(k) = P(i), where rad = A007947 and primorial P = A002110.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..74468.

Michael De Vlieger, Efficient Mathematica constructor program for A055932

Mathematica

(* Load function f in the linked constructor a-file *)
Differences@ Union@ Flatten@ f[8]

Prog

(Python)
from functools import lru_cache
from itertools import count
from sympy import prime, integer_log, primorial
from oeis_sequences.OEISsequences import bisection
def A376690(n):
    @lru_cache(maxsize=None)
    def g(x, m): return sum(g(x//(prime(m)**i), m-1) for i in range(1, integer_log(x, prime(m))[0]+1)) if m-1 else x.bit_length()-1
    def f(x):
        c = n-1+x
        for k in count(1):
            if primorial(k)>x:
                break
            c -= g(x, k)
        return c
    return -(m:=bisection(f, n, n))+bisection(lambda x:f(x)+1, m, m) # Chai Wah Wu, Mar 18 2026

Crossrefs

Cf. A002110, A007947, A055932, A178799.

Sequence in context: A117728 A172309 A130453 * A259981 A391066 A070705

Adjacent sequences: A376687 A376688 A376689 * A376691 A376692 A376693

Keyword

nonn,easy

Author

Michael De Vlieger, Oct 13 2024

Status

approved