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A323652 Numbers m having at least one divisor d such that m divides sigma(d). 3
1, 6, 12, 28, 56, 120, 360, 496, 672, 992, 2016, 8128, 16256, 30240, 32760, 60480, 65520, 120960, 131040, 523776, 1571328, 2178540, 4357080, 8714160, 23569920, 33550336, 45532800, 47139840, 67100672, 91065600, 94279680, 142990848, 182131200, 285981696 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Generalization of multiperfect numbers (A007691).

Multiperfect numbers (A007691) are terms. If m is a k-multiperfect number and d divides k (for k > 1 and d > 1), then d*m is also a term.

Number 1379454720 is the smallest number with two divisors d with this property (459818240 and 1379454720). Another such number is 153003540480 with divisors 51001180160 and 153003540480. Is there a number with three divisors d with this property?

Supersequence of A081756.

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

12 is a term because 6 divides 12 and simultaneously 12 divides sigma(6) = 12.

PROG

(MAGMA) [n: n in [1..10000] | #[d: d in Divisors(n) | SumOfDivisors(d) mod n eq 0] gt 0]

(PARI) isok(n) = {fordiv(n, d, if (!(sigma(d) % n), return (1)); ); return (0); } \\ Michel Marcus, Jan 21 2019

CROSSREFS

Cf. A000203, A007691, A081756, A323653.

Sequence in context: A183026 A146005 A325812 * A223346 A109510 A034715

Adjacent sequences:  A323649 A323650 A323651 * A323653 A323654 A323655

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Jan 21 2019

STATUS

approved

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Last modified March 8 09:33 EST 2021. Contains 341948 sequences. (Running on oeis4.)