

A342970


Numbers m such that both m^21 and m^2 are refactorable numbers (A033950) and that m^2 has more divisors than m^21.


2



3591, 4545, 5481, 6975, 8415, 9639, 11319, 11583, 11745, 12225, 12735, 16065, 18711, 24255, 24759, 30015, 31671, 39105, 40257, 41535, 41769, 44631, 44865, 52065, 52569, 53055, 54975, 56511, 60255, 60705, 64071, 64575, 69825, 72009, 73665, 76095, 81081, 81855, 87129
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OFFSET

1,1


COMMENTS

Numbers m such that m^21 is divisible by d(m^21), m^2 is divisible by d(m^2) and d(m^2) > d(m^21), d = A000005.
The smallest term not divisible by 3 is a(1048) = 2907025.


LINKS

Jianing Song, Table of n, a(n) for n = 1..1500


EXAMPLE

5481 is a term since 5481^21 is divisible by d(5481^21) = 40, 5481^2 is divisible by d(5481^2) = 63, and 63 > 40.
2907025 is a term since 2907025^21 is divisible by d(2907025^21) = 96, 2907025^2 is divisible by d(2907025^2) = 125, and 125 > 96.


PROG

(PARI) isA342970(n) = if(n>1, my(d1 = numdiv(n^21), d2 = numdiv(n^2)); !((n^21) % d1) && !(n^2 % d2) && d2 > d1, 0)


CROSSREFS

Cf. A000005, A033950, A342969.
Sequence in context: A249537 A156845 A174851 * A284970 A183007 A251087
Adjacent sequences: A342967 A342968 A342969 * A342971 A342972 A342973


KEYWORD

nonn


AUTHOR

Jianing Song, Apr 01 2021


STATUS

approved



