A349952 The smallest of 3 consecutive integers such that the first is divisible by the square of a prime, the second is divisible by the cube of a prime, and the third is divisible by the fourth power of a prime.

350, 1375, 2023, 11150, 11374, 12446, 13310, 13374, 15631, 17575, 19550, 21248, 21463, 21950, 22382, 25038, 25623, 26702, 27950, 29790, 29887, 31211, 31374, 32750, 33614, 33775, 35623, 36124, 40815, 41742, 43550, 45374, 47383, 48734, 49374, 49975, 54350, 54511

Offset

1,1

References

George E. Andrews, Number Theory, Exercise 5 at p. 71 (Dover ed. 1994)

Links

Table of n, a(n) for n=1..38.

Maple

q:= n-> min(map(t-> max(seq(i[2], i=ifactors(t)[2])), [$n..n+2])-[$1..3])>0:
select(q, [$1..60000])[];  # Alois P. Heinz, May 02 2022

Mathematica

okQ[{a_, b_, c_}]:=Max[FactorInteger[a][[All, 2]]]>1&&Max[FactorInteger[b][[All, 2]]]>2&&Max[FactorInteger[c][[All, 2]]]>3; Select[Partition[Range[ 100000], 3, 1], okQ][[All, 1]]

Prog

(Python)
from sympy import factorint
from itertools import count, islice
def agen(): # generator of terms
    kvec, fvec = [2, 3, 4], [{2: 1}, {3: 1}, {2: 2}]
    for k in count(5):
        if all(max(fvec[i].values())>=2+i for i in range(3)): yield kvec[0]
        kvec, fvec = kvec[1:] + [k], fvec[1:] + [factorint(k)]
print(list(islice(agen(), 40))) # Michael S. Branicky, May 02 2022

Crossrefs

Sequence in context: A074055 A304282 A190645 * A108776 A184609 A322668

Adjacent sequences: A349949 A349950 A349951 * A349953 A349954 A349955

Keyword

nonn

Author

Harvey P. Dale, May 02 2022

Status

approved